Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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×#901 | C2 | semidirect |
| 3. C2×C3×C4×C8 | C2 | semidirect |
| 4. #5110 | C2 | semidirect |
| 5. #4924 | C2 | semidirect |
| 6. #4688 | C2 | semidirect |
| 7. C8×D12 | C2 | semidirect |
| 32. C2×C4×C8 | D3 | semidirect |
| 43. C2×C3×C8 | D4 | semidirect |
| 107. C2×C8 | D12 | semidirect |
| 123. C3×C4 | #131 | semidirect |
| 159. C4 | #901 | semidirect |
| 162. C3 | #2931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#901 | 2 |
| #5477 | 2 |
| C2×C3×C4×C8 | 2 |
| #5110 | 2 |
| #4924 | 2 |
| #4688 | 2 |
| C8×D12 | 2 |
| #2931 | 3 |