Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2049 conjugacy classes of subgroups; only the 396 normal subgroups are shown.
This group has 2049 conjugacy classes of subgroups — too many to draw. Only its 396 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. C3×#5798 | C2 | semidirect |
| 3. C2×#63581 | C2 | semidirect |
| 4. #10591232 | C2 | semidirect |
| 9. C2×#3830 | C4 | semidirect |
| 10. C2×D4×C3⋊D3 | C4 | semidirect |
| 12. C2×C3×#217 | C22 | semidirect |
| 14. C3×#926 | C22 | semidirect |
| 15. #63581 | C22 | semidirect |
| 19. #5798 | D3 | semidirect |
| 23. C23×C3⋊D3 | C2×C4 | semidirect |
| 28. C2×#638 | C2×C4 | semidirect |
| 30. C22×C3⋊Dic3 | C2×C4 | semidirect |
| 34. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 35. C2×C4×C3⋊D3 | C2×C4 | semidirect |
| 36. C2×#634 | C2×C4 | semidirect |
| 59. C2×#217 | C2×D3 | semidirect |
| 61. #926 | C2×D3 | semidirect |
| 243. C32 | #2883 | semidirect |
| 287. C3 | #82546 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64361 | 2 |
| C3×#5798 | 2 |
| C2×#63581 | 2 |
| #10591232 | 2 |
| #82546 | 3 |