Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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×#904 | C2 | semidirect |
| 2. C2×#901 | C2 | semidirect |
| 3. #5510 | C2 | semidirect |
| 4. C2×C3×#107 | C2 | semidirect |
| 5. #4966 | C2 | semidirect |
| 6. #4887 | C2 | semidirect |
| 7. #4886 | C2 | semidirect |
| 8. #4883 | C2 | semidirect |
| 37. C2×#107 | D3 | semidirect |
| 54. C2×C3×C8 | D4 | semidirect |
| 138. C2×C8 | D12 | semidirect |
| 210. C3 | #3061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| C2×#901 | 2 |
| #5510 | 2 |
| C2×C3×#107 | 2 |
| #4966 | 2 |
| #4887 | 2 |
| #4886 | 2 |
| #4883 | 2 |
| #3061 | 3 |