Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
376 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 6. #4851 | C2 | semidirect |
| 7. #4850 | C2 | semidirect |
| 8. #4829 | C2 | semidirect |
| 51. C2×Dic6 | Q8 | semidirect |
| 208. C3 | #3078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5470 | 2 |
| C2×C4×Dic6 | 2 |
| C3×#423 | 2 |
| #5121 | 2 |
| #5120 | 2 |
| #4851 | 2 |
| #4850 | 2 |
| #4829 | 2 |
| #3078 | 3 |