Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
444 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×C32×Q16 | C2 | semidirect |
| 4. C2×#3756 | C2 | semidirect |
| 5. #63662 | C2 | semidirect |
| 7. #63643 | C2 | semidirect |
| 25. C2×C3×Q16 | D3 | semidirect |
| 69. C2×C3⋊D3 | Q16 | semidirect |
| 79. C2×Q16 | C3⋊D3 | semidirect |
| 133. C32 | #451 | semidirect |
| 168. C3 | #5186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C3⋊D3 | 2 |
| C2×C32×Q16 | 2 |
| #64155 | 2 |
| C2×#3756 | 2 |
| #63662 | 2 |
| #63647 | 2 |
| #63643 | 2 |
| #5186 | 3 |