Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
164 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 49 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. #5188 | C2 | semidirect |
| 2. C2×#828 | C2 | semidirect |
| 3. C2×D3×C16 | C2 | semidirect |
| 5. C3×#358 | C2 | semidirect |
| 6. #4509 | C2 | semidirect |
| 7. #4490 | C2 | semidirect |
| 27. #358 | D3 | semidirect |
| 47. C3⋊C16 | D4 | semidirect |
| 103. C2×D3 | SD32 | semidirect |
| 145. C3 | #2217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5188 | 2 |
| C2×#828 | 2 |
| C2×D3×C16 | 2 |
| #4883 | 2 |
| C3×#358 | 2 |
| #4509 | 2 |
| #4490 | 2 |
| #2217 | 3 |