Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
164 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 69 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×#798 | C2 | semidirect |
| 2. C2×D3×C16 | C2 | semidirect |
| 4. C3×C4⋊C16 | C2 | semidirect |
| 5. (C2×D3)⋊C16 | C2 | semidirect |
| 6. (C2×D3)⋊C16 | C2 | semidirect |
| 7. #4461 | C2 | semidirect |
| 25. C4⋊C16 | D3 | semidirect |
| 47. C3⋊C16 | D4 | semidirect |
| 103. C2×D3 | M32 | semidirect |
| 145. C3 | #2168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#798 | 2 |
| C2×D3×C16 | 2 |
| C8×D12 | 2 |
| C3×C4⋊C16 | 2 |
| (C2×D3)⋊C16 | 2 |
| #4461 | 2 |
| #2168 | 3 |