Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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×#919 | C2 | semidirect |
| 2. C2×C3×SD32 | C2 | semidirect |
| 3. #5157 | C2 | semidirect |
| 4. C2×#826 | C2 | semidirect |
| 5. #4564 | C2 | semidirect |
| 6. #4509 | C2 | semidirect |
| 7. (C2×D3)⋊C16 | C2 | semidirect |
| 25. C2×SD32 | D3 | semidirect |
| 41. C3×Q16 | D4 | semidirect |
| 50. D24 | D4 | semidirect |
| 101. Q16 | #67 | semidirect |
| 172. C3 | #2186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#919 | 2 |
| C2×C3×SD32 | 2 |
| #5157 | 2 |
| C2×#826 | 2 |
| #4564 | 2 |
| #4509 | 2 |
| (C2×D3)⋊C16 | 2 |
| #2186 | 3 |