Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 18. #822 | C4 | semidirect |
| 21. C8×Dic3 | C4 | semidirect |
| 22. #808 | C4 | semidirect |
| 23. #807 | C4 | semidirect |
| 154. C3 | #1772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#405 | 2 |
| C2×#822 | 2 |
| #5101 | 2 |
| C2×C8×Dic3 | 2 |
| #4998 | 2 |
| #4555 | 2 |
| #4532 | 2 |
| #1772 | 3 |