Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
294 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22627005 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22626059 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #17989706 | — | 2 | 2 | no | — |
| 4 | C2×#14556653 | — | 2 | 2 | no | — |
| 5 | C4×#11924036 | C22 | 1 | 1 | yes | characteristic |
| 6 | #17989533 | C4 | 1 | 1 | yes | characteristic |
| 7 | #127×D73 | C4 | 1 | 1 | yes | characteristic |
| 8 | #14556688 | — | 2 | 4 | no | — |
| 9 | #14556687 | — | 4 | 2 | no | — |
| 10 | #14556686 | — | 4 | 2 | no | — |
| 11 | C2×#11924036 | D4 | 1 | 2 | yes | — |
| 12 | C2×C4⋊#64408 | — | 2 | 1 | no | — |
| 13 | C2×C4⋊#64408 | — | 4 | 1 | no | — |
| 14 | #14556653 | — | 4 | 2 | no | — |
| 15 | #14556653 | — | 4 | 2 | no | — |
| 16 | C4×#10596833 | — | 4 | 1 | no | — |
| 17 | C2×D4×D73 | — | 2 | 1 | no | — |
| 18 | C2×D4×D73 | — | 4 | 1 | no | — |
| 19 | #14556588 | C8 | 1 | 1 | yes | characteristic |
| 20 | #14556587 | — | 2 | 1 | no | — |
| 21 | #14556587 | — | 4 | 1 | no | — |
| 22 | C42×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 23 | #127×C73 | C8 | 1 | 1 | yes | characteristic |
| 24 | #11924040 | — | 4 | 4 | no | — |
| 25 | C22×#64408 | — | 4 | 1 | no | — |
| 26 | #11924036 | — | 2 | 2 | no | — |
| 27 | #11924036 | D8 | 1 | 2 | yes | — |
| 28 | #11924036 | SD16 | 1 | 2 | yes | — |
| 29 | C2×#10596833 | — | 2 | 2 | no | — |
| 30 | C4⋊#64408 | — | 4 | 2 | no | — |
| 31 | C4⋊#64408 | — | 8 | 2 | no | — |
| 32 | C23×D73 | — | 4 | 1 | no | — |
| 33 | C2×D292 | — | 2 | 1 | no | — |
| 34 | C2×D292 | — | 4 | 1 | no | — |
| 35 | C2×C22⋊D73 | — | 4 | 2 | no | — |
| 36 | C2×C22⋊D73 | — | 4 | 1 | no | — |
| 37 | D4×D73 | — | 4 | 2 | no | — |
| 38 | D4×D73 | — | 4 | 2 | no | — |
| 39 | D4×D73 | — | 8 | 2 | no | — |
| 40 | D4×D73 | — | 8 | 2 | no | — |
| 41 | C2×C4×D73 | — | 2 | 1 | no | — |
| 42 | C2×C4×D73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 43 | C4×Dic73 | — | 2 | 1 | no | — |
| 44 | C4×Dic73 | M16 | 1 | 1 | yes | characteristic |
| 45 | C2×D4×C73 | — | 2 | 1 | no | — |
| 46 | C2×D4×C73 | — | 4 | 1 | no | — |
| 47 | C42×C73 | C2×C8 | 1 | 1 | yes | characteristic |
| 48 | C23×C73 | — | 4 | 1 | no | — |
| 49 | C22×D73 | — | 4 | 1 | no | — |
| 50 | C22×D73 | — | 8 | 2 | no | — |
| 51 | C22×D73 | — | 8 | 2 | no | — |
| 52 | C22×D73 | — | 8 | 1 | no | — |
| 53 | C22×D73 | — | 8 | 1 | no | — |
| 54 | C22×D73 | #100 | 1 | 1 | yes | characteristic |
| 55 | C2×#64408 | — | 8 | 2 | no | — |
| 56 | C2×#64408 | — | 8 | 1 | no | — |
| 57 | D4×C73 | — | 4 | 2 | no | — |
| 58 | D4×C73 | — | 8 | 2 | no | — |
| 59 | C2×C4×C73 | — | 2 | 1 | no | — |
| 60 | C2×C4×C73 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 61 | C22⋊D73 | — | 8 | 4 | no | — |
| 62 | C22⋊D73 | — | 8 | 2 | no | — |
| 63 | C2×Dic73 | — | 2 | 1 | no | — |
| 64 | C2×Dic73 | #99 | 1 | 1 | yes | characteristic |
| 65 | D292 | — | 4 | 2 | no | — |
| 66 | D292 | — | 8 | 2 | no | — |
| 67 | C4×D73 | — | 2 | 2 | no | — |
| 68 | C4×D73 | — | 2 | 2 | no | — |
| 69 | C4×D73 | #102 | 1 | 2 | yes | — |
| 70 | C4×D73 | #104 | 1 | 2 | yes | — |
| 71 | #10596833 | — | 2 | 2 | no | — |
| 72 | #10596833 | — | 2 | 2 | no | — |
| 73 | C22×C73 | — | 8 | 2 | no | — |
| 74 | C22×C73 | — | 8 | 1 | no | — |
| 75 | C22×C73 | #323 | 1 | 1 | yes | characteristic |
| 76 | C2×D73 | — | 2 | 1 | no | — |
| 77 | C2×D73 | — | 2 | 1 | no | — |
| 78 | C2×D73 | — | 8 | 2 | no | — |
| 79 | C2×D73 | — | 8 | 1 | no | — |
| 80 | C2×D73 | — | 16 | 2 | no | — |
| 81 | C2×D73 | — | 16 | 1 | no | — |
| 82 | C2×D73 | — | 16 | 1 | no | — |
| 83 | C2×D73 | #329 | 1 | 1 | yes | characteristic |
| 84 | C2×D73 | #331 | 1 | 1 | yes | characteristic |
| 85 | #64408 | — | 16 | 1 | no | — |
| 86 | C4×C73 | — | 2 | 2 | no | — |
| 87 | C4×C73 | D4⋊C8 | 1 | 2 | yes | — |
| 88 | Dic73 | — | 2 | 2 | no | — |
| 89 | Dic73 | #327 | 1 | 2 | yes | — |
| 90 | #7107 | — | 73 | 1 | no | maximal, Sylow |
| 91 | C2×C73 | — | 2 | 1 | no | — |
| 92 | C2×C73 | — | 16 | 1 | no | — |
| 93 | C2×C73 | #1270 | 1 | 1 | yes | characteristic |
| 94 | D73 | — | 2 | 1 | no | — |
| 95 | D73 | — | 16 | 1 | no | — |
| 96 | D73 | #1357 | 1 | 1 | yes | characteristic |
| 97 | D73 | #1359 | 1 | 1 | yes | characteristic |
| 98 | #1957 | — | 73 | 1 | no | — |
| 99 | #1376 | — | 73 | 2 | no | — |
| 100 | C73 | #7107 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 101 | C2×#127 | — | 73 | 1 | no | — |
| 102 | C2×M32 | — | 146 | 2 | no | — |
| 103 | C2×#102 | — | 146 | 2 | no | — |
| 104 | C2×C4×C8 | — | 73 | 1 | no | — |
| 105 | #384 | — | 73 | 1 | no | — |
| 106 | C22×D4 | — | 292 | 1 | no | — |
| 107 | C22×D4 | — | 146 | 1 | no | — |
| 108 | C22×C8 | — | 73 | 2 | no | — |
| 109 | #127 | — | 292 | 1 | no | — |
| 110 | #127 | — | 73 | 1 | no | — |
| 111 | #127 | — | 146 | 1 | no | — |
| 112 | #127 | #10596842 | 1 | 1 | yes | characteristic |
| 113 | C2×C4⋊C4 | — | 292 | 1 | no | — |
| 114 | C2×C4⋊C4 | — | 146 | 1 | no | — |
| 115 | C2×C42 | — | 73 | 1 | no | — |
| 116 | M32 | — | 292 | 2 | no | — |
| 117 | M32 | — | 146 | 4 | no | — |
| 118 | C2×C16 | — | 292 | 2 | no | — |
| 119 | #102 | — | 292 | 2 | no | — |
| 120 | #102 | — | 292 | 2 | no | — |
| 121 | C4×C8 | — | 292 | 1 | no | — |
| 122 | C24 | — | 292 | 1 | no | — |
| 123 | C2×D4 | — | 2 | 1 | no | — |
| 124 | C2×D4 | — | 4 | 1 | no | — |
| 125 | C2×D4 | — | 292 | 1 | no | — |
| 126 | C2×D4 | — | 292 | 2 | no | — |
| 127 | C2×D4 | — | 292 | 2 | no | — |
| 128 | C2×D4 | — | 292 | 1 | no | — |
| 129 | C2×D4 | — | 292 | 2 | no | — |
| 130 | C2×D4 | — | 584 | 2 | no | — |
| 131 | C2×D4 | — | 584 | 2 | no | — |
| 132 | C2×D4 | — | 146 | 1 | no | — |
| 133 | C22×C4 | — | 292 | 1 | no | — |
| 134 | C22×C4 | — | 73 | 1 | no | — |
| 135 | C22×C4 | — | 146 | 1 | no | — |
| 136 | C2×C8 | — | 73 | 2 | no | — |
| 137 | C2×C8 | — | 73 | 2 | no | — |
| 138 | C2×C8 | — | 146 | 2 | no | — |
| 139 | C2×C8 | — | 146 | 2 | no | — |
| 140 | C4⋊C4 | — | 292 | 2 | no | — |
| 141 | C4⋊C4 | — | 584 | 2 | no | — |
| 142 | C42 | — | 73 | 1 | no | — |
| 143 | C42 | — | 146 | 1 | no | — |
| 144 | C42 | C2×#10596842 | 1 | 1 | yes | characteristic |
| 145 | C16 | — | 292 | 4 | no | — |
| 146 | C23 | — | 4 | 1 | no | — |
| 147 | C23 | — | 292 | 1 | no | — |
| 148 | C23 | — | 584 | 1 | no | — |
| 149 | C23 | — | 584 | 1 | no | — |
| 150 | C23 | — | 584 | 2 | no | — |
| 151 | C23 | — | 584 | 2 | no | — |
| 152 | C23 | — | 73 | 1 | no | — |
| 153 | D4 | — | 4 | 2 | no | — |
| 154 | D4 | — | 8 | 2 | no | — |
| 155 | D4 | — | 292 | 2 | no | — |
| 156 | D4 | — | 584 | 2 | no | — |
| 157 | D4 | — | 584 | 2 | no | — |
| 158 | D4 | — | 584 | 4 | no | — |
| 159 | C2×C4 | — | 2 | 1 | no | — |
| 160 | C2×C4 | — | 584 | 1 | no | — |
| 161 | C2×C4 | — | 584 | 2 | no | — |
| 162 | C2×C4 | — | 73 | 1 | no | — |
| 163 | C2×C4 | — | 73 | 2 | no | — |
| 164 | C2×C4 | — | 73 | 2 | no | — |
| 165 | C2×C4 | — | 146 | 2 | no | — |
| 166 | C2×C4 | — | 146 | 2 | no | — |
| 167 | C2×C4 | — | 146 | 1 | no | — |
| 168 | C2×C4 | C22⋊#10596842 | 1 | 1 | yes | characteristic |
| 169 | C8 | — | 146 | 2 | no | — |
| 170 | C8 | — | 146 | 2 | no | — |
| 171 | C22 | — | 8 | 2 | no | — |
| 172 | C22 | — | 8 | 1 | no | — |
| 173 | C22 | — | 584 | 2 | no | — |
| 174 | C22 | — | 584 | 1 | no | — |
| 175 | C22 | — | 73 | 1 | no | — |
| 176 | C22 | — | 73 | 1 | no | — |
| 177 | C22 | — | 1168 | 1 | no | — |
| 178 | C22 | — | 1168 | 1 | no | — |
| 179 | C22 | — | 1168 | 2 | no | — |
| 180 | C22 | — | 146 | 1 | no | — |
| 181 | C22 | — | 146 | 1 | no | — |
| 182 | C22 | #17989672 | 1 | 1 | yes | characteristic |
| 183 | C4 | — | 2 | 2 | no | — |
| 184 | C4 | — | 73 | 2 | no | — |
| 185 | C4 | — | 1168 | 1 | no | — |
| 186 | C4 | — | 146 | 2 | no | — |
| 187 | C4 | D4⋊#10596842 | 1 | 2 | yes | — |
| 188 | C2 | — | 2 | 1 | no | — |
| 189 | C2 | — | 16 | 1 | no | — |
| 190 | C2 | — | 73 | 1 | no | — |
| 191 | C2 | — | 73 | 1 | no | — |
| 192 | C2 | — | 1168 | 1 | no | — |
| 193 | C2 | — | 146 | 1 | no | — |
| 194 | C2 | #22626930 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22627005 | C2 | semidirect |
| 100. C73 | #7107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627005 | 2 |
| #22626059 | 2 |
| #7107 | 73 |