Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×D24 | C2 | semidirect |
| 2. C2×#874 | C2 | semidirect |
| 3. C2×C4×D12 | C2 | semidirect |
| 4. C2×C3×C4⋊C8 | C2 | semidirect |
| 5. C2×#821 | C2 | semidirect |
| 6. #4843 | C2 | direct (N × H) |
| 18. C2×D24 | C22 | semidirect |
| 20. #874 | C22 | semidirect |
| 22. C4×D12 | C22 | semidirect |
| 23. C3×C4⋊C8 | C22 | semidirect |
| 24. #821 | C22 | semidirect |
| 29. C2×C4⋊C8 | D3 | semidirect |
| 46. C2×D12 | D4 | semidirect |
| 74. C4⋊C8 | C2×D3 | semidirect |
| 86. C2×C3×C4 | D8 | semidirect |
| 102. D12 | C2×D4 | semidirect |
| 147. C3×C4 | C2×D8 | semidirect |
| 172. C2×C4 | D24 | semidirect |
| 180. C2×C3 | #459 | semidirect |
| 201. C4 | C2×D24 | semidirect |
| 204. C3 | C2×#459 | semidirect |
| 207. C2 | #4843 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D24 | 2 |
| C2×#874 | 2 |
| C2×C4×D12 | 2 |
| C2×C3×C4⋊C8 | 2 |
| C2×#821 | 2 |
| #4843 | 2 |
| C2×#459 | 3 |