Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
996 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 365 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 |
|---|---|---|
| 13. #64078 | C4 | semidirect |
| 89. C32×C4 | #103 | semidirect |
| 146. C3×C4 | #810 | semidirect |
| 150. C32 | #1956 | semidirect |
| 179. C4 | #63637 | semidirect |
| 182. C3 | #69579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64078 | 2 |
| C32×#384 | 2 |
| C2×#63637 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| #69579 | 3 |