Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
| 3. #5088 | C2 | semidirect |
| 4. #5087 | C2 | semidirect |
| 5. #5067 | C2 | semidirect |
| 6. #5066 | C2 | semidirect |
| 7. #5027 | C2 | semidirect |
| 8. #5027 | C2 | semidirect |
| 9. #5026 | C2 | semidirect |
| 10. C4×#215 | C2 | semidirect |
| 11. #5024 | C2 | semidirect |
| 42. #557 | D3 | semidirect |
| 120. C3×Q8 | #41 | semidirect |
| 198. Q8 | #239 | semidirect |
| 243. C3 | #3368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#557 | 2 |
| #5577 | 2 |
| #5088 | 2 |
| #5087 | 2 |
| #5067 | 2 |
| #5066 | 2 |
| #5027 | 2 |
| #5026 | 2 |
| C4×#215 | 2 |
| #5024 | 2 |
| #3368 | 3 |