Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
614 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 614 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×#3832 | C2 | semidirect |
| 2. C2×#3796 | C2 | semidirect |
| 3. C2×C3×#216 | C2 | semidirect |
| 4. C2×C3×#215 | C2 | semidirect |
| 5. #63950 | C2 | direct (N × H) |
| 6. C2×#3717 | C2 | semidirect |
| 7. C2×#3714 | C2 | semidirect |
| 8. C2×#3710 | C2 | semidirect |
| 13. #3832 | C22 | semidirect |
| 23. #3796 | C22 | semidirect |
| 24. C3×#216 | C22 | semidirect |
| 25. C3×#215 | C22 | semidirect |
| 28. #3717 | C22 | semidirect |
| 29. #3714 | C22 | semidirect |
| 30. #3710 | C22 | semidirect |
| 38. C2×#216 | D3 | semidirect |
| 40. C2×#215 | D3 | semidirect |
| 109. #216 | C2×D3 | semidirect |
| 111. #215 | C2×D3 | semidirect |
| 198. C2×C32 | #135 | semidirect |
| 256. C32 | C2×#135 | semidirect |
| 283. C2×C3 | #916 | semidirect |
| 284. C2×C3 | #919 | semidirect |
| 307. C3 | C2×#916 | semidirect |
| 308. C3 | C2×#919 | semidirect |
| 312. C2 | #63950 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3832 | 2 |
| C2×#3796 | 2 |
| C2×C3×#216 | 2 |
| C2×C3×#215 | 2 |
| #63950 | 2 |
| C2×#3717 | 2 |
| C2×#3714 | 2 |
| C2×#3710 | 2 |
| C2×#919 | 3 |
| C2×#916 | 3 |