Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 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. #5713 | C2 | semidirect |
| 2. #5542 | C2 | semidirect |
| 4. #5155 | C2 | semidirect |
| 5. #5153 | C2 | semidirect |
| 6. #5076 | C2 | semidirect |
| 7. C4×#214 | C2 | semidirect |
| 8. #4849 | C2 | semidirect |
| 9. #4830 | C2 | semidirect |
| 10. #4767 | C2 | semidirect |
| 11. #4758 | C2 | semidirect |
| 245. C3 | #3394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5713 | 2 |
| #5542 | 2 |
| C3×#459 | 2 |
| #5155 | 2 |
| #5153 | 2 |
| #5076 | 2 |
| C4×#214 | 2 |
| #4849 | 2 |
| #4830 | 2 |
| #4767 | 2 |
| #4758 | 2 |
| #3394 | 3 |