Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#904 | C2 | semidirect |
| 2. #5477 | C2 | semidirect |
| 3. C2×C3×#97 | C2 | semidirect |
| 4. #4715 | C2 | semidirect |
| 5. #4712 | C2 | semidirect |
| 24. C2×#97 | D3 | semidirect |
| 33. C2×C3×C8 | D4 | semidirect |
| 80. C2×C8 | D12 | semidirect |
| 122. C3 | #3150 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| #5477 | 2 |
| C2×C3×#97 | 2 |
| #4715 | 2 |
| #4712 | 2 |
| #3150 | 3 |