Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
402 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 4. C2×#816 | C2 | semidirect |
| 5. #4929 | C2 | semidirect |
| 6. C3×#336 | C2 | semidirect |
| 7. #4551 | C2 | semidirect |
| 20. C2×#204 | C4 | semidirect |
| 33. #336 | D3 | semidirect |
| 55. C2×Dic6 | C2×C4 | semidirect |
| 61. C2×C3×C8 | C2×C4 | semidirect |
| 101. C2×C3×C4 | SD16 | semidirect |
| 156. C2×C8 | C4×D3 | semidirect |
| 218. C2×C4 | #204 | semidirect |
| 258. C3 | #1877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#204 | 2 |
| C2×C4×D12 | 2 |
| C2×#821 | 2 |
| C2×#816 | 2 |
| #4929 | 2 |
| C3×#336 | 2 |
| #4551 | 2 |
| #1877 | 3 |