Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #5542 | C2 | semidirect |
| 2. D4×Dic6 | C2 | semidirect |
| 5. #5019 | C2 | semidirect |
| 6. #5007 | C2 | semidirect |
| 7. #4875 | C2 | semidirect |
| 8. #4765 | C2 | semidirect |
| 9. #4757 | C2 | semidirect |
| 10. #4681 | C2 | semidirect |
| 11. #4679 | C2 | semidirect |
| 239. C3 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5542 | 2 |
| D4×Dic6 | 2 |
| C3×C4×D8 | 2 |
| #5153 | 2 |
| #5019 | 2 |
| #5007 | 2 |
| #4875 | 2 |
| #4765 | 2 |
| #4757 | 2 |
| #4681 | 2 |
| #4679 | 2 |
| #3367 | 3 |