Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1008 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 233 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. C32×C4×C4⋊C4 | C2 | semidirect |
| 3. C2×#63632 | C2 | semidirect |
| 4. C4×#3748 | C2 | semidirect |
| 13. #64084 | C4 | semidirect |
| 14. #64083 | C4 | semidirect |
| 17. #64078 | C4 | semidirect |
| 23. C3×C4×C4⋊C4 | D3 | semidirect |
| 49. #3748 | D4 | semidirect |
| 95. C4×C4⋊C4 | C3⋊D3 | semidirect |
| 133. C32×C4 | #104 | semidirect |
| 220. C3×C4 | #805 | semidirect |
| 224. C32 | #1980 | semidirect |
| 268. C4 | #63632 | semidirect |
| 271. C3 | #69492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595948 | 2 |
| C32×C4×C4⋊C4 | 2 |
| C2×#63632 | 2 |
| C4×#3748 | 2 |
| #69492 | 3 |