Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 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. C3×#557 | C2 | semidirect |
| 4. #5078 | C2 | semidirect |
| 6. #5064 | C2 | semidirect |
| 9. #5024 | C2 | semidirect |
| 10. #5021 | C2 | semidirect |
| 11. #5020 | C2 | semidirect |
| 42. #557 | D3 | semidirect |
| 75. #215 | Q8 | semidirect |
| 118. C3×Q8 | C2×Q8 | semidirect |
| 137. C3⋊C8 | C2×Q8 | semidirect |
| 191. Q8 | D3×Q8 | semidirect |
| 228. C3 | #3386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#557 | 2 |
| Q8×D12 | 2 |
| #5087 | 2 |
| #5078 | 2 |
| #5066 | 2 |
| #5064 | 2 |
| #5026 | 2 |
| C4×#215 | 2 |
| #5024 | 2 |
| #5021 | 2 |
| #5020 | 2 |
| #3386 | 3 |