Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
550 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 160 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. C22×C3×Dic6 | C2 | semidirect |
| 3. C2×#3748 | C2 | semidirect |
| 4. C2×#3718 | C2 | semidirect |
| 5. #63827 | C2 | direct (N × H) |
| 6. C2×#3715 | C2 | semidirect |
| 20. C2×C3×Dic6 | C22 | semidirect |
| 21. #3748 | C22 | semidirect |
| 23. #3718 | C22 | semidirect |
| 24. #3715 | C22 | semidirect |
| 28. C22×Dic6 | D3 | semidirect |
| 82. C2×Dic6 | C2×D3 | semidirect |
| 154. C2×C32 | #137 | semidirect |
| 199. C32 | C2×#137 | semidirect |
| 225. C2×C3 | #942 | semidirect |
| 226. C2×C3 | #951 | semidirect |
| 241. C3 | C2×#942 | semidirect |
| 242. C3 | C2×#951 | semidirect |
| 245. C2 | #63827 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#235 | 2 |
| C22×C3×Dic6 | 2 |
| C2×#3748 | 2 |
| C2×#3718 | 2 |
| #63827 | 2 |
| C2×#3715 | 2 |
| C2×#951 | 3 |
| C2×#942 | 3 |