Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
550 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 144 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×C3×D3×Q8 | C2 | semidirect |
| 3. C2×#3755 | C2 | semidirect |
| 4. C2×C3×#216 | C2 | semidirect |
| 5. #63948 | C2 | direct (N × H) |
| 6. C2×#3718 | C2 | semidirect |
| 7. C2×#3717 | C2 | semidirect |
| 8. C2×#3711 | C2 | semidirect |
| 14. C3×D3×Q8 | C22 | semidirect |
| 24. #3755 | C22 | semidirect |
| 26. C3×#216 | C22 | semidirect |
| 28. #3718 | C22 | semidirect |
| 29. #3717 | C22 | semidirect |
| 30. #3711 | C22 | semidirect |
| 33. C2×D3×Q8 | D3 | semidirect |
| 38. C2×#216 | D3 | semidirect |
| 86. D3×Q8 | C2×D3 | semidirect |
| 104. #216 | C2×D3 | semidirect |
| 189. C2×C32 | #137 | semidirect |
| 241. C32 | C2×#137 | semidirect |
| 268. C2×C3 | #918 | semidirect |
| 269. C2×C3 | #942 | semidirect |
| 288. C3 | C2×#918 | semidirect |
| 289. C3 | C2×#942 | semidirect |
| 292. C2 | #63948 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×Q8 | 2 |
| C2×#3799 | 2 |
| C2×#3755 | 2 |
| C2×C3×#216 | 2 |
| #63948 | 2 |
| C2×#3718 | 2 |
| C2×#3717 | 2 |
| C2×#3711 | 2 |
| C2×#942 | 3 |
| C2×#918 | 3 |