Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
362 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3753 | C2 | semidirect |
| 2. C3×#940 | C2 | semidirect |
| 3. C2×C3×#213 | C2 | semidirect |
| 4. #63911 | C2 | semidirect |
| 5. C2×#3714 | C2 | semidirect |
| 6. C2×#3713 | C2 | semidirect |
| 7. Dic3×C3⋊C8 | C2 | semidirect |
| 26. #940 | D3 | semidirect |
| 33. C2×#213 | D3 | semidirect |
| 54. C3⋊(C3⋊C8) | D4 | semidirect |
| 55. C3×C3⋊C8 | D4 | semidirect |
| 98. C3×Dic3 | D8 | semidirect |
| 149. C3⋊C8 | #67 | semidirect |
| 199. Dic3 | #213 | semidirect |
| 200. C32 | #493 | semidirect |
| 248. C3 | #5073 | semidirect |
| 249. C3 | #5151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3753 | 2 |
| C3×#940 | 2 |
| C2×C3×#213 | 2 |
| #63911 | 2 |
| C2×#3714 | 2 |
| C2×#3713 | 2 |
| Dic3×C3⋊C8 | 2 |
| #5151 | 3 |
| #5073 | 3 |