Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
869 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 869 conjugacy classes of subgroups — too many to draw. Only its 156 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×#64121 | C2 | semidirect |
| 2. C2×#63810 | C2 | semidirect |
| 3. C2×C3×#827 | C2 | semidirect |
| 4. C2×C3×#826 | C2 | semidirect |
| 5. #10591035 | C2 | direct (N × H) |
| 6. C2×#63551 | C2 | semidirect |
| 7. C2×#63548 | C2 | semidirect |
| 8. C2×#63542 | C2 | semidirect |
| 16. #64121 | C22 | semidirect |
| 23. #63810 | C22 | semidirect |
| 24. C3×#827 | C22 | semidirect |
| 25. C3×#826 | C22 | semidirect |
| 28. #63551 | C22 | semidirect |
| 29. #63548 | C22 | semidirect |
| 30. #63542 | C22 | semidirect |
| 40. C2×#827 | D3 | semidirect |
| 41. C2×#826 | D3 | semidirect |
| 117. #827 | C2×D3 | semidirect |
| 118. #826 | C2×D3 | semidirect |
| 328. C2×C32 | #508 | semidirect |
| 394. C32 | C2×#508 | semidirect |
| 425. C2×C3 | #4912 | semidirect |
| 426. C2×C3 | #4916 | semidirect |
| 446. C3 | C2×#4912 | semidirect |
| 447. C3 | C2×#4916 | semidirect |
| 451. C2 | #10591035 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64121 | 2 |
| C2×#63810 | 2 |
| C2×C3×#827 | 2 |
| C2×C3×#826 | 2 |
| #10591035 | 2 |
| C2×#63551 | 2 |
| C2×#63548 | 2 |
| C2×#63542 | 2 |
| C2×#4916 | 3 |
| C2×#4912 | 3 |