Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
874 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 874 conjugacy classes of subgroups — too many to draw. Only its 196 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. #10596223 | C2 | semidirect |
| 2. C3×#5752 | C2 | semidirect |
| 3. C3×#5140 | C2 | semidirect |
| 4. #10590634 | C2 | semidirect |
| 5. #10590633 | C2 | semidirect |
| 6. #10590632 | C2 | semidirect |
| 7. C2×#63546 | C2 | semidirect |
| 14. #64113 | C22 | semidirect |
| 15. C2×#3745 | C22 | semidirect |
| 17. C3×#904 | C22 | semidirect |
| 18. C2×C3×D24 | C22 | semidirect |
| 19. C3×#812 | C22 | semidirect |
| 20. C2×C3×C3⋊C16 | C22 | semidirect |
| 21. #63551 | C22 | semidirect |
| 22. #63549 | C22 | semidirect |
| 23. #63548 | C22 | semidirect |
| 24. #63546 | C22 | semidirect |
| 25. #63546 | C22 | semidirect |
| 30. #5752 | D3 | semidirect |
| 36. #5140 | D3 | semidirect |
| 81. #904 | C2×D3 | semidirect |
| 85. C2×D24 | C2×D3 | semidirect |
| 93. #812 | C2×D3 | semidirect |
| 94. C2×C3⋊C16 | C2×D3 | semidirect |
| 296. C32 | #3415 | semidirect |
| 335. C3 | #82013 | semidirect |
| 336. C3 | #84007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596223 | 2 |
| C3×#5752 | 2 |
| C3×#5140 | 2 |
| #10590634 | 2 |
| #10590633 | 2 |
| #10590632 | 2 |
| C2×#63546 | 2 |
| #84007 | 3 |
| #82013 | 3 |