Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2064 conjugacy classes of subgroups; only the 537 normal subgroups are shown.
This group has 2064 conjugacy classes of subgroups — too many to draw. Only its 537 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. #10592946 | C2 | semidirect |
| 3. #10592920 | C2 | semidirect |
| 4. #10592919 | C2 | semidirect |
| 5. #10592650 | C2 | semidirect |
| 9. C23×C3⋊Dic3 | C22 | semidirect |
| 10. C32×#120 | C4 | semidirect |
| 14. C2×#3757 | C22 | semidirect |
| 15. C2×C4⋊(C3⋊Dic3) | C22 | semidirect |
| 16. C2×C4×C3⋊Dic3 | C22 | semidirect |
| 17. #63658 | C22 | semidirect |
| 25. C24×C32 | C2×C4 | semidirect |
| 35. C32×C22⋊C4 | C2×C4 | semidirect |
| 45. C3×#120 | Dic3 | semidirect |
| 81. C24×C3 | C2×Dic3 | semidirect |
| 91. C3×C22⋊C4 | C2×Dic3 | semidirect |
| 115. #120 | C3⋊Dic3 | semidirect |
| 151. C24 | C2×C3⋊Dic3 | semidirect |
| 165. C22⋊C4 | C2×C3⋊Dic3 | semidirect |
| 182. C32 | #2375 | semidirect |
| 224. C3 | #82580 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#120 | 2 |
| #10592946 | 2 |
| #10592920 | 2 |
| #10592919 | 2 |
| #10592650 | 2 |
| #82580 | 3 |