Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 14. #63628 | C4 | semidirect |
| 107. C32 | #2176 | semidirect |
| 125. C3 | #69338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63628 | 2 |
| #10592572 | 2 |
| C32×#367 | 2 |
| #10589368 | 2 |
| #10589358 | 2 |
| #69338 | 3 |