Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 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. #5567 | C2 | semidirect |
| 5. #5020 | C2 | semidirect |
| 7. #4854 | C2 | semidirect |
| 8. #4792 | C2 | semidirect |
| 10. #4681 | C2 | semidirect |
| 11. C8×Dic6 | C2 | semidirect |
| 136. Dic6 | SD16 | semidirect |
| 232. C3 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5567 | 2 |
| D4×Dic6 | 2 |
| C3×C4×SD16 | 2 |
| #5162 | 2 |
| #5020 | 2 |
| #5019 | 2 |
| #4854 | 2 |
| #4792 | 2 |
| #4758 | 2 |
| #4681 | 2 |
| C8×Dic6 | 2 |
| #3359 | 3 |