Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 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. #5570 | C2 | semidirect |
| 5. #5031 | C2 | semidirect |
| 7. #4857 | C2 | semidirect |
| 8. #4790 | C2 | semidirect |
| 10. #4681 | C2 | semidirect |
| 11. C8×Dic6 | C2 | semidirect |
| 226. C3 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5570 | 2 |
| #5542 | 2 |
| C3×C4×SD16 | 2 |
| #5166 | 2 |
| #5031 | 2 |
| #5007 | 2 |
| #4857 | 2 |
| #4790 | 2 |
| #4768 | 2 |
| #4681 | 2 |
| C8×Dic6 | 2 |
| #3364 | 3 |