Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
610 conjugacy classes of subgroups; only the 382 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 382 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. C3×Q8×Dic3 | C2 | semidirect |
| 5. #5812 | C3 | direct (N × H) |
| 6. C2×C32×Q8 | C4 | semidirect |
| 17. Q8×Dic3 | C2×C3 | semidirect |
| 27. C2×C3×Q8 | Dic3 | semidirect |
| 28. C2×C3×Q8 | C3×C4 | semidirect |
| 65. C2×Q8 | C3×Dic3 | semidirect |
| 85. C32 | #519 | semidirect |
| 106. C3 | #5812 | direct (N × H) |
| 107. C3 | C3×#519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q8 | 2 |
| C3×Q8×Dic3 | 2 |
| C3×#926 | 2 |
| C3×#519 | 3 |
| #5812 | 3 |