Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
594 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 136 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×Q8×C3⋊D3 | C2 | semidirect |
| 3. C2×C3×#216 | C2 | semidirect |
| 4. C2×C3×#215 | C2 | semidirect |
| 5. #63951 | C2 | direct (N × H) |
| 6. C2×#3719 | C2 | semidirect |
| 7. C2×#3716 | C2 | semidirect |
| 8. C2×#3712 | C2 | semidirect |
| 13. Q8×C3⋊D3 | C22 | semidirect |
| 24. C3×#216 | C22 | semidirect |
| 25. C3×#215 | C22 | semidirect |
| 28. #3719 | C22 | semidirect |
| 29. #3716 | C22 | semidirect |
| 30. #3712 | C22 | semidirect |
| 39. C2×#216 | D3 | semidirect |
| 40. C2×#215 | D3 | semidirect |
| 110. #216 | C2×D3 | semidirect |
| 111. #215 | C2×D3 | semidirect |
| 197. C2×C32 | #137 | semidirect |
| 251. C32 | C2×#137 | semidirect |
| 278. C2×C3 | #915 | semidirect |
| 279. C2×C3 | #918 | semidirect |
| 298. C3 | C2×#915 | semidirect |
| 299. C3 | C2×#918 | semidirect |
| 302. C2 | #63951 | direct (N × H) |
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×#3796 | 2 |
| C2×C3×#216 | 2 |
| C2×C3×#215 | 2 |
| #63951 | 2 |
| C2×#3719 | 2 |
| C2×#3716 | 2 |
| C2×#3712 | 2 |
| C2×#918 | 3 |
| C2×#915 | 3 |