Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
254 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 68 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×#3756 | C2 | semidirect |
| 2. C3×Q8×Dic3 | C2 | semidirect |
| 5. Dic3⋊(C3⋊C8) | C2 | semidirect |
| 6. #63567 | C2 | semidirect |
| 25. Q8×Dic3 | D3 | semidirect |
| 184. C32 | #464 | semidirect |
| 223. C3 | #5028 | semidirect |
| 224. C3 | #5166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3756 | 2 |
| C3×Q8×Dic3 | 2 |
| C2×C3×#215 | 2 |
| #63860 | 2 |
| Dic3⋊(C3⋊C8) | 2 |
| #63567 | 2 |
| #63562 | 2 |
| #5166 | 3 |
| #5028 | 3 |