Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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. #5722 | C2 | semidirect |
| 4. #5093 | C2 | semidirect |
| 6. #4854 | C2 | semidirect |
| 7. #4853 | C2 | semidirect |
| 8. #4849 | C2 | semidirect |
| 9. #4831 | C2 | semidirect |
| 228. C3 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5722 | 2 |
| #5542 | 2 |
| C3×#476 | 2 |
| #5093 | 2 |
| C4×#214 | 2 |
| #4854 | 2 |
| #4853 | 2 |
| #4849 | 2 |
| #4831 | 2 |
| #4767 | 2 |
| #4765 | 2 |
| #3369 | 3 |