Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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. C2×C3×Q32 | C2 | semidirect |
| 4. #4564 | C2 | semidirect |
| 5. #4504 | C2 | semidirect |
| 16. C2×Q32 | D3 | semidirect |
| 71. C2×D3 | Q32 | semidirect |
| 102. C3 | #2216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q32 | 2 |
| #5188 | 2 |
| C2×D3×C16 | 2 |
| #4564 | 2 |
| #4504 | 2 |
| #2216 | 3 |