Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1440 conjugacy classes of subgroups; only the 393 normal subgroups are shown.
This group has 1440 conjugacy classes of subgroups — too many to draw. Only its 393 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 |
|---|---|---|
| 6. #10592552 | C2 | direct (N × H) |
| 15. C2×#3746 | C4 | semidirect |
| 46. #3746 | C2×C4 | semidirect |
| 142. C2×C32 | #441 | semidirect |
| 173. C32 | C2×#441 | semidirect |
| 190. C2×C3 | #4853 | semidirect |
| 202. C3 | C2×#4853 | semidirect |
| 203. C2 | #10592552 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3746 | 2 |
| C2×#64096 | 2 |
| C2×C32×#106 | 2 |
| C2×#63642 | 2 |
| C2×#63637 | 2 |
| #10592552 | 2 |
| C2×#4853 | 3 |