Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×C3×M32 | C2 | semidirect |
| 3. C2×#798 | C2 | semidirect |
| 4. #4549 | C2 | semidirect |
| 5. (C2×D3)⋊C16 | C2 | semidirect |
| 6. Dic3⋊C16 | C2 | semidirect |
| 7. Dic3×C16 | C2 | semidirect |
| 23. C2×M32 | D3 | semidirect |
| 45. C3×C16 | D4 | semidirect |
| 96. C16 | #67 | semidirect |
| 109. Dic3 | M32 | semidirect |
| 145. C3 | #2169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×M32 | 2 |
| C8×#67 | 2 |
| C2×#798 | 2 |
| #4549 | 2 |
| (C2×D3)⋊C16 | 2 |
| Dic3⋊C16 | 2 |
| Dic3×C16 | 2 |
| #2169 | 3 |