Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 21. C4×#157 | C8 | semidirect |
| 120. C32 | #1831 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×#157 | 2 |
| #10593726 | 2 |
| #10590090 | 2 |
| #1831 | 9 |