Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 196 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 | #5672 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #5060 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #4702 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#329 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #4465 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #1660 | — | 3 | 1 | no | maximal, Sylow |
| 7 | C3×#124 | C22 | 1 | 1 | yes | characteristic |
| 8 | #944 | — | 2 | 1 | no | — |
| 9 | C2×#216 | — | 2 | 1 | no | — |
| 10 | #935 | — | 2 | 1 | no | — |
| 11 | C2×#214 | — | 2 | 1 | no | — |
| 12 | #879 | — | 2 | 2 | no | — |
| 13 | #878 | — | 2 | 2 | no | — |
| 14 | #870 | C22 | 1 | 2 | yes | — |
| 15 | #869 | C22 | 1 | 1 | yes | characteristic |
| 16 | C3×#97 | C22 | 1 | 2 | yes | — |
| 17 | #818 | — | 2 | 2 | no | — |
| 18 | #817 | — | 2 | 2 | no | — |
| 19 | #803 | C22 | 1 | 1 | yes | characteristic |
| 20 | #563 | — | 3 | 1 | no | — |
| 21 | #501 | — | 3 | 2 | no | — |
| 22 | #497 | — | 3 | 1 | no | — |
| 23 | #330 | — | 3 | 2 | no | — |
| 24 | #329 | D3 | 1 | 1 | yes | characteristic |
| 25 | C2×C3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 26 | C2×C3×D4 | D4 | 1 | 1 | yes | characteristic |
| 27 | C22×Dic3 | — | 2 | 1 | no | — |
| 28 | C2×Dic6 | — | 2 | 1 | no | — |
| 29 | C2×Dic6 | — | 2 | 1 | no | — |
| 30 | C2×C3×C8 | — | 2 | 2 | no | — |
| 31 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 32 | C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 33 | #217 | — | 2 | 2 | no | — |
| 34 | #217 | — | 2 | 1 | no | — |
| 35 | #216 | — | 4 | 2 | no | — |
| 36 | #214 | — | 4 | 2 | no | — |
| 37 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 38 | C4⋊Dic3 | D4 | 1 | 2 | yes | — |
| 39 | C4⋊Dic3 | D4 | 1 | 2 | yes | — |
| 40 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 41 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 42 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 43 | C4×Dic3 | — | 2 | 1 | no | — |
| 44 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 45 | C2×Q16 | — | 6 | 1 | no | — |
| 46 | C2×SD16 | — | 6 | 1 | no | — |
| 47 | C4⋊Q8 | — | 3 | 1 | no | — |
| 48 | C4⋊Q8 | — | 6 | 1 | no | — |
| 49 | #126 | — | 6 | 2 | no | — |
| 50 | #125 | — | 3 | 2 | no | — |
| 51 | #124 | C2×D3 | 1 | 1 | yes | characteristic |
| 52 | #123 | — | 6 | 1 | no | — |
| 53 | C22⋊Q8 | — | 6 | 2 | no | — |
| 54 | #107 | — | 6 | 2 | no | — |
| 55 | #106 | — | 6 | 2 | no | — |
| 56 | #97 | — | 3 | 1 | no | — |
| 57 | #97 | C2×D3 | 1 | 2 | yes | — |
| 58 | C23×C3 | — | 2 | 1 | no | — |
| 59 | C3×Q8 | — | 4 | 1 | no | — |
| 60 | C3×D4 | — | 4 | 1 | no | — |
| 61 | C2×C3×C4 | — | 2 | 1 | no | — |
| 62 | C2×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 63 | C2×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 64 | C2×Dic3 | — | 2 | 2 | no | — |
| 65 | C2×Dic3 | — | 2 | 2 | no | — |
| 66 | C2×Dic3 | — | 4 | 1 | no | — |
| 67 | C2×Dic3 | — | 8 | 1 | no | — |
| 68 | Dic6 | — | 4 | 1 | no | — |
| 69 | Dic6 | — | 4 | 1 | no | — |
| 70 | Dic6 | — | 8 | 1 | no | — |
| 71 | C3×C8 | — | 2 | 4 | no | — |
| 72 | C3⋊C8 | — | 2 | 2 | no | — |
| 73 | C2×Q8 | — | 6 | 1 | no | — |
| 74 | C2×Q8 | — | 6 | 1 | no | — |
| 75 | C2×Q8 | D12 | 1 | 1 | yes | characteristic |
| 76 | C2×D4 | D12 | 1 | 1 | yes | characteristic |
| 77 | C22×C4 | — | 6 | 1 | no | — |
| 78 | Q16 | — | 12 | 2 | no | — |
| 79 | SD16 | — | 12 | 2 | no | — |
| 80 | C2×C8 | — | 2 | 2 | no | — |
| 81 | C2×C8 | — | 6 | 1 | no | — |
| 82 | C4⋊C4 | — | 3 | 2 | no | — |
| 83 | C4⋊C4 | — | 3 | 2 | no | — |
| 84 | C4⋊C4 | — | 6 | 2 | no | — |
| 85 | C4⋊C4 | — | 6 | 2 | no | — |
| 86 | C4⋊C4 | — | 6 | 2 | no | — |
| 87 | C4⋊C4 | — | 6 | 2 | no | — |
| 88 | C22⋊C4 | — | 2 | 2 | no | — |
| 89 | C22⋊C4 | — | 6 | 2 | no | — |
| 90 | C22⋊C4 | — | 6 | 1 | no | — |
| 91 | C42 | — | 6 | 1 | no | — |
| 92 | C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 93 | C22×C3 | — | 4 | 1 | no | — |
| 94 | C22×C3 | — | 4 | 2 | no | — |
| 95 | C22×C3 | #120 | 1 | 1 | yes | characteristic |
| 96 | C3×C4 | — | 2 | 1 | no | — |
| 97 | C3×C4 | — | 2 | 2 | no | — |
| 98 | C3×C4 | — | 4 | 1 | no | — |
| 99 | Dic3 | — | 4 | 2 | no | — |
| 100 | Dic3 | — | 4 | 2 | no | — |
| 101 | Dic3 | — | 8 | 1 | no | — |
| 102 | C23 | — | 2 | 1 | no | — |
| 103 | Q8 | — | 4 | 1 | no | — |
| 104 | Q8 | — | 12 | 1 | no | — |
| 105 | Q8 | — | 12 | 1 | no | — |
| 106 | Q8 | — | 24 | 1 | no | — |
| 107 | D4 | — | 4 | 1 | no | — |
| 108 | C2×C4 | — | 2 | 1 | no | — |
| 109 | C2×C4 | — | 6 | 2 | no | — |
| 110 | C2×C4 | — | 6 | 2 | no | — |
| 111 | C2×C4 | — | 12 | 1 | no | — |
| 112 | C2×C4 | — | 24 | 1 | no | — |
| 113 | C2×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 114 | C2×C4 | D3×D4 | 1 | 2 | yes | — |
| 115 | C8 | — | 2 | 4 | no | — |
| 116 | C8 | — | 6 | 2 | no | — |
| 117 | C2×C3 | — | 8 | 1 | no | — |
| 118 | C2×C3 | #453 | 1 | 1 | yes | characteristic |
| 119 | C2×C3 | #456 | 1 | 2 | yes | — |
| 120 | C22 | — | 4 | 1 | no | — |
| 121 | C22 | — | 4 | 2 | no | — |
| 122 | C22 | #882 | 1 | 1 | yes | characteristic |
| 123 | C4 | — | 2 | 1 | no | — |
| 124 | C4 | — | 2 | 2 | no | — |
| 125 | C4 | — | 4 | 1 | no | — |
| 126 | C4 | — | 12 | 2 | no | — |
| 127 | C4 | — | 12 | 2 | no | — |
| 128 | C4 | — | 24 | 1 | no | — |
| 129 | C3 | #1660 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 130 | C2 | — | 8 | 1 | no | — |
| 131 | C2 | #4747 | 1 | 1 | yes | characteristic |
| 132 | C2 | #4826 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #4702 | C2 | semidirect |
| 5. #4465 | C2 | semidirect |
| 129. C3 | #1660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5672 | 2 |
| #5060 | 2 |
| #4702 | 2 |
| C3×#329 | 2 |
| #4465 | 2 |
| #1660 | 3 |