Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
291 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 291 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. Q8×C3⋊Dic3 | C2 | semidirect |
| 2. C2×C3×#215 | C2 | semidirect |
| 4. #63572 | C2 | semidirect |
| 5. #63563 | C2 | semidirect |
| 20. C2×#215 | D3 | semidirect |
| 27. C32×Q8 | D4 | semidirect |
| 66. C3⋊Dic3 | SD16 | semidirect |
| 77. C3×Q8 | #67 | semidirect |
| 130. C32 | #460 | semidirect |
| 133. Q8 | #625 | semidirect |
| 163. C3 | #5163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊Dic3 | 2 |
| C2×C3×#215 | 2 |
| #63914 | 2 |
| #63572 | 2 |
| #63563 | 2 |
| #5163 | 3 |