Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
174 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 174 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×D48 | C2 | semidirect |
| 2. C2×D3×C16 | C2 | semidirect |
| 3. #4883 | C2 | semidirect |
| 4. C3×#366 | C2 | semidirect |
| 5. #4491 | C2 | semidirect |
| 19. #366 | D3 | semidirect |
| 32. C3×C16 | D4 | semidirect |
| 68. C16 | D12 | semidirect |
| 75. C2×D3 | D16 | semidirect |
| 109. C3 | #2215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D48 | 2 |
| C2×D3×C16 | 2 |
| #4883 | 2 |
| C3×#366 | 2 |
| #4491 | 2 |
| #2215 | 3 |