Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
438 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×C4×D12 | C2 | semidirect |
| 3. C2×#821 | C2 | semidirect |
| 4. C2×#821 | C2 | semidirect |
| 5. #4939 | C2 | semidirect |
| 6. C3×#336 | C2 | semidirect |
| 7. #4551 | C2 | semidirect |
| 22. C2×D24 | C4 | semidirect |
| 33. #336 | D3 | semidirect |
| 50. C2×D12 | C2×C4 | semidirect |
| 61. C2×C3×C8 | C2×C4 | semidirect |
| 110. C2×C3×C4 | D8 | semidirect |
| 130. D12 | C22⋊C4 | semidirect |
| 162. C2×C8 | C4×D3 | semidirect |
| 236. C2×C4 | D24 | semidirect |
| 283. C3 | #1879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D24 | 2 |
| C2×C4×D12 | 2 |
| C2×#821 | 2 |
| #4939 | 2 |
| C3×#336 | 2 |
| #4551 | 2 |
| #1879 | 3 |