Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
444 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #5798 | C2 | semidirect |
| 3. C2×C3×#100 | C2 | semidirect |
| 4. #5131 | C2 | semidirect |
| 5. #4555 | C2 | semidirect |
| 13. #940 | C4 | semidirect |
| 22. C2×#100 | D3 | semidirect |
| 38. C2×D12 | C2×C4 | semidirect |
| 44. C4⋊Dic3 | D4 | semidirect |
| 47. C4×Dic3 | C2×C4 | semidirect |
| 168. C3 | #1887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#940 | 2 |
| #5798 | 2 |
| C2×C3×#100 | 2 |
| #5131 | 2 |
| #4555 | 2 |
| #1887 | 3 |