Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #5805 | C2 | semidirect |
| 2. C2×#940 | C2 | semidirect |
| 3. C2×#908 | C2 | semidirect |
| 4. C2×C3×#100 | C2 | semidirect |
| 5. C2×#825 | C2 | semidirect |
| 6. #5131 | C2 | semidirect |
| 7. #4555 | C2 | semidirect |
| 35. C2×#100 | D3 | semidirect |
| 60. C2×D12 | D4 | semidirect |
| 61. C2×D12 | D4 | semidirect |
| 63. C2×Dic6 | D4 | semidirect |
| 67. C3×M16 | D4 | semidirect |
| 72. C4⋊Dic3 | D4 | semidirect |
| 75. C4×Dic3 | D4 | semidirect |
| 171. M16 | #67 | semidirect |
| 269. C3 | #2002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5805 | 2 |
| C2×#940 | 2 |
| C2×#908 | 2 |
| C2×C3×#100 | 2 |
| C2×#825 | 2 |
| #5131 | 2 |
| #4555 | 2 |
| #2002 | 3 |