Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
773 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 773 conjugacy classes of subgroups — too many to draw. Only its 148 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. #10594684 | C2 | semidirect |
| 2. C2×#63625 | C2 | semidirect |
| 3. C3×#4904 | C2 | semidirect |
| 4. #10590629 | C2 | semidirect |
| 5. #10590246 | C2 | semidirect |
| 6. #10590236 | C2 | semidirect |
| 10. C3×#904 | C22 | semidirect |
| 14. #63802 | C22 | semidirect |
| 15. #63797 | C22 | semidirect |
| 17. C2×C32×C16 | C22 | semidirect |
| 18. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 19. #63625 | C22 | semidirect |
| 20. C3×Dic24 | C22 | semidirect |
| 21. C3×#800 | C22 | semidirect |
| 22. C3×D48 | C22 | semidirect |
| 23. #63550 | C22 | semidirect |
| 24. #63547 | C22 | semidirect |
| 25. #63545 | C22 | semidirect |
| 33. #4904 | D3 | semidirect |
| 67. #904 | C2×D3 | semidirect |
| 74. C2×C3×C16 | C2×D3 | semidirect |
| 81. Dic24 | C2×D3 | semidirect |
| 82. #800 | C2×D3 | semidirect |
| 83. D48 | C2×D3 | semidirect |
| 172. C2×C16 | D32 | semidirect |
| 247. C32 | #3414 | semidirect |
| 284. C3 | #82030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10594684 | 2 |
| C2×#63625 | 2 |
| C3×#4904 | 2 |
| #10590629 | 2 |
| #10590246 | 2 |
| #10590236 | 2 |
| #82030 | 3 |