Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
222 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 29 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 | #22626971 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22626064 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #17989686 | — | 2 | 2 | no | — |
| 4 | #17989591 | C22 | 1 | 1 | yes | characteristic |
| 5 | C2×#14556656 | — | 2 | 2 | no | — |
| 6 | C42×#64408 | C4 | 1 | 1 | yes | characteristic |
| 7 | #17989138 | C4 | 1 | 1 | yes | characteristic |
| 8 | #14556687 | — | 4 | 2 | no | — |
| 9 | C2×#11924038 | D4 | 1 | 2 | yes | — |
| 10 | C2×C4×#64408 | — | 2 | 1 | no | — |
| 11 | C2×C4×#64408 | — | 4 | 1 | no | — |
| 12 | C4⋊#10596833 | — | 4 | 1 | no | — |
| 13 | #14556656 | — | 4 | 4 | no | — |
| 14 | C2×#11924029 | — | 2 | 1 | no | — |
| 15 | #14556588 | C8 | 1 | 1 | yes | characteristic |
| 16 | #14556580 | — | 2 | 1 | no | — |
| 17 | #14556566 | — | 4 | 1 | no | — |
| 18 | #14556553 | — | 4 | 1 | no | — |
| 19 | C42×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 20 | C4⋊Q8×C73 | C8 | 1 | 1 | yes | characteristic |
| 21 | #11924040 | — | 8 | 2 | no | — |
| 22 | C22×#64408 | — | 4 | 1 | no | — |
| 23 | #11924038 | — | 4 | 2 | no | — |
| 24 | C2×#10596833 | — | 2 | 2 | no | — |
| 25 | C4×#64408 | — | 2 | 2 | no | — |
| 26 | C4×#64408 | — | 4 | 1 | no | — |
| 27 | C4×#64408 | — | 4 | 4 | no | — |
| 28 | #11924029 | — | 4 | 2 | no | — |
| 29 | #11924029 | — | 4 | 2 | no | — |
| 30 | C2×D292 | — | 2 | 1 | no | — |
| 31 | C2×D292 | — | 4 | 1 | no | — |
| 32 | C2×D292 | — | 4 | 1 | no | — |
| 33 | C2×C4×D73 | — | 2 | 1 | no | — |
| 34 | C2×C4×D73 | — | 4 | 1 | no | — |
| 35 | C2×C4×D73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 36 | #11924005 | — | 4 | 2 | no | — |
| 37 | C4×Dic73 | — | 2 | 1 | no | — |
| 38 | C4×Dic73 | M16 | 1 | 1 | yes | characteristic |
| 39 | C2×Q8×C73 | — | 2 | 1 | no | — |
| 40 | C4⋊C4×C73 | — | 4 | 1 | no | — |
| 41 | C42×C73 | C2×C8 | 1 | 1 | yes | characteristic |
| 42 | C22×D73 | — | 4 | 1 | no | — |
| 43 | C22×D73 | #100 | 1 | 1 | yes | characteristic |
| 44 | C2×#64408 | — | 4 | 2 | no | — |
| 45 | C2×#64408 | — | 4 | 4 | no | — |
| 46 | Q8×C73 | — | 4 | 2 | no | — |
| 47 | C2×C4×C73 | — | 2 | 1 | no | — |
| 48 | C2×C4×C73 | — | 4 | 1 | no | — |
| 49 | C2×C4×C73 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 50 | C2×Dic73 | — | 2 | 1 | no | — |
| 51 | C2×Dic73 | #99 | 1 | 1 | yes | characteristic |
| 52 | D292 | — | 4 | 2 | no | — |
| 53 | D292 | — | 8 | 2 | no | — |
| 54 | D292 | — | 8 | 2 | no | — |
| 55 | C4×D73 | — | 2 | 1 | no | — |
| 56 | C4×D73 | — | 2 | 1 | no | — |
| 57 | C4×D73 | — | 4 | 2 | no | — |
| 58 | C4×D73 | — | 8 | 1 | no | — |
| 59 | C4×D73 | — | 8 | 1 | no | — |
| 60 | #10596833 | — | 4 | 2 | no | — |
| 61 | C22×C73 | #323 | 1 | 1 | yes | characteristic |
| 62 | C2×D73 | — | 2 | 1 | no | — |
| 63 | C2×D73 | — | 4 | 1 | no | — |
| 64 | C2×D73 | — | 8 | 2 | no | — |
| 65 | C2×D73 | — | 8 | 1 | no | — |
| 66 | #64408 | — | 4 | 4 | no | — |
| 67 | C4×C73 | — | 2 | 2 | no | — |
| 68 | C4×C73 | — | 2 | 1 | no | — |
| 69 | C4×C73 | — | 8 | 1 | no | — |
| 70 | Dic73 | — | 4 | 1 | no | — |
| 71 | Dic73 | #353 | 1 | 1 | yes | characteristic |
| 72 | Dic73 | #355 | 1 | 1 | yes | characteristic |
| 73 | #7357 | — | 73 | 1 | no | maximal, Sylow |
| 74 | C2×C73 | — | 2 | 1 | no | — |
| 75 | C2×C73 | #1318 | 1 | 1 | yes | characteristic |
| 76 | D73 | — | 4 | 1 | no | — |
| 77 | D73 | — | 16 | 1 | no | — |
| 78 | #1962 | — | 73 | 1 | no | — |
| 79 | #1327 | — | 73 | 2 | no | — |
| 80 | C73 | #7357 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 81 | #532 | — | 73 | 1 | no | — |
| 82 | #423 | — | 73 | 1 | no | — |
| 83 | C2×#104 | — | 146 | 2 | no | — |
| 84 | C43 | — | 73 | 1 | no | — |
| 85 | #349 | — | 146 | 2 | no | — |
| 86 | C2×#41 | — | 146 | 1 | no | — |
| 87 | C2×M16 | — | 73 | 2 | no | — |
| 88 | C4⋊Q8 | #10596842 | 1 | 1 | yes | characteristic |
| 89 | #127 | — | 73 | 1 | no | — |
| 90 | #124 | — | 146 | 1 | no | — |
| 91 | #121 | — | 292 | 1 | no | — |
| 92 | C4×D4 | — | 292 | 1 | no | — |
| 93 | C2×C42 | — | 292 | 1 | no | — |
| 94 | C2×C42 | — | 73 | 1 | no | — |
| 95 | C2×C42 | — | 146 | 1 | no | — |
| 96 | M32 | — | 292 | 2 | no | — |
| 97 | C4⋊C8 | — | 292 | 1 | no | — |
| 98 | #104 | — | 292 | 4 | no | — |
| 99 | #41 | — | 292 | 2 | no | — |
| 100 | #41 | — | 292 | 2 | no | — |
| 101 | C2×Q8 | — | 2 | 1 | no | — |
| 102 | C2×D4 | — | 292 | 1 | no | — |
| 103 | C2×D4 | — | 292 | 1 | no | — |
| 104 | C2×D4 | — | 146 | 1 | no | — |
| 105 | C22×C4 | — | 292 | 1 | no | — |
| 106 | C22×C4 | — | 292 | 1 | no | — |
| 107 | C22×C4 | — | 73 | 1 | no | — |
| 108 | C22×C4 | — | 146 | 1 | no | — |
| 109 | M16 | — | 292 | 2 | no | — |
| 110 | C2×C8 | — | 146 | 2 | no | — |
| 111 | C4⋊C4 | — | 4 | 1 | no | — |
| 112 | C22⋊C4 | — | 292 | 2 | no | — |
| 113 | C42 | — | 292 | 4 | no | — |
| 114 | C42 | — | 292 | 1 | no | — |
| 115 | C42 | — | 73 | 1 | no | — |
| 116 | C42 | — | 146 | 1 | no | — |
| 117 | C42 | — | 146 | 2 | no | — |
| 118 | C42 | C2×#10596842 | 1 | 1 | yes | characteristic |
| 119 | C16 | — | 584 | 2 | no | — |
| 120 | C23 | — | 292 | 1 | no | — |
| 121 | C23 | — | 73 | 1 | no | — |
| 122 | Q8 | — | 4 | 2 | no | — |
| 123 | D4 | — | 292 | 2 | no | — |
| 124 | D4 | — | 584 | 2 | no | — |
| 125 | D4 | — | 584 | 2 | no | — |
| 126 | C2×C4 | — | 2 | 1 | no | — |
| 127 | C2×C4 | — | 4 | 1 | no | — |
| 128 | C2×C4 | — | 292 | 2 | no | — |
| 129 | C2×C4 | — | 292 | 4 | no | — |
| 130 | C2×C4 | — | 292 | 2 | no | — |
| 131 | C2×C4 | — | 584 | 1 | no | — |
| 132 | C2×C4 | — | 584 | 1 | no | — |
| 133 | C2×C4 | — | 73 | 1 | no | — |
| 134 | C2×C4 | — | 146 | 1 | no | — |
| 135 | C2×C4 | — | 146 | 1 | no | — |
| 136 | C2×C4 | — | 146 | 1 | no | — |
| 137 | C2×C4 | C22⋊#10596842 | 1 | 1 | yes | characteristic |
| 138 | C8 | — | 292 | 2 | no | — |
| 139 | C22 | — | 292 | 1 | no | — |
| 140 | C22 | — | 584 | 2 | no | — |
| 141 | C22 | — | 584 | 1 | no | — |
| 142 | C22 | — | 146 | 1 | no | — |
| 143 | C22 | #17989672 | 1 | 1 | yes | characteristic |
| 144 | C4 | — | 2 | 2 | no | — |
| 145 | C4 | — | 2 | 1 | no | — |
| 146 | C4 | — | 8 | 1 | no | — |
| 147 | C4 | — | 292 | 1 | no | — |
| 148 | C4 | — | 292 | 4 | no | — |
| 149 | C4 | — | 73 | 1 | no | — |
| 150 | C4 | — | 73 | 1 | no | — |
| 151 | C2 | — | 2 | 1 | no | — |
| 152 | C2 | — | 292 | 1 | no | — |
| 153 | C2 | — | 1168 | 1 | no | — |
| 154 | C2 | #22626958 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22626971 | C2 | semidirect |
| 80. C73 | #7357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626971 | 2 |
| #22626064 | 2 |
| #7357 | 73 |