Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
364 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 197 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. #4679 | C2 | semidirect |
| 7. C8×Dic6 | C2 | semidirect |
| 35. C2×C3×C8 | Q8 | semidirect |
| 84. C2×C8 | Dic6 | semidirect |
| 131. C3 | #2960 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5470 | 2 |
| C2×C3×C4×C8 | 2 |
| #5102 | 2 |
| #5101 | 2 |
| #4924 | 2 |
| #4679 | 2 |
| C8×Dic6 | 2 |
| #2960 | 3 |