Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1837 conjugacy classes of subgroups; only the 322 normal subgroups are shown.
This group has 1837 conjugacy classes of subgroups — too many to draw. Only its 322 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×#5825 | C2 | semidirect |
| 3. C3×#5243 | C2 | semidirect |
| 4. C3×#5240 | C2 | semidirect |
| 6. #84124 | C3 | direct (N × H) |
| 12. C22×C3×Dic6 | C22 | semidirect |
| 15. C3×#935 | C22 | semidirect |
| 16. C3×#926 | C22 | semidirect |
| 18. C3×#834 | C22 | semidirect |
| 23. #5825 | C2×C3 | semidirect |
| 26. #5243 | C2×C3 | semidirect |
| 27. #5240 | C2×C3 | semidirect |
| 67. C22×Dic6 | C22×C3 | semidirect |
| 75. #935 | C22×C3 | semidirect |
| 76. #926 | C22×C3 | semidirect |
| 79. #834 | C22×C3 | semidirect |
| 285. C32 | #3028 | semidirect |
| 324. C3 | #84124 | direct (N × H) |
| 325. C3 | C3×#3028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#585 | 2 |
| C3×#5825 | 2 |
| C3×#5243 | 2 |
| C3×#5240 | 2 |
| C3×#3028 | 3 |
| #84124 | 3 |