Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
933 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 933 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×#64128 | C2 | semidirect |
| 2. C2×#63797 | C2 | semidirect |
| 3. C2×C3×#828 | C2 | semidirect |
| 4. #10591040 | C2 | direct (N × H) |
| 5. C2×#63546 | C2 | semidirect |
| 6. C2×#63544 | C2 | semidirect |
| 10. C2×C32×Q16 | C22 | semidirect |
| 13. #64128 | C22 | semidirect |
| 14. C2×#3745 | C22 | semidirect |
| 19. #63797 | C22 | semidirect |
| 20. C3×#828 | C22 | semidirect |
| 21. C2×C3×C3⋊C16 | C22 | semidirect |
| 22. #63546 | C22 | semidirect |
| 23. #63544 | C22 | semidirect |
| 28. C2×#828 | D3 | semidirect |
| 46. C32×Q16 | C23 | semidirect |
| 51. #3745 | C23 | semidirect |
| 57. C3×C3⋊C16 | C23 | semidirect |
| 63. C2×C3×Q16 | C2×D3 | semidirect |
| 81. #828 | C2×D3 | semidirect |
| 83. C2×C3⋊C16 | C2×D3 | semidirect |
| 137. C3×Q16 | C22×D3 | semidirect |
| 158. C3⋊C16 | C22×D3 | semidirect |
| 175. C2×Q16 | D32 | semidirect |
| 228. C2×C32 | #509 | semidirect |
| 246. Q16 | C2×D32 | semidirect |
| 281. C32 | C2×#509 | semidirect |
| 307. C2×C3 | #4914 | semidirect |
| 327. C3 | C2×#4914 | semidirect |
| 331. C2 | #10591040 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64128 | 2 |
| C2×#63797 | 2 |
| C2×C3×#828 | 2 |
| #10591040 | 2 |
| C2×#63546 | 2 |
| C2×#63544 | 2 |
| C2×#4914 | 3 |