Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
624 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
|---|---|---|
| 225. C32 | #2064 | semidirect |
| 266. C3 | #70679 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#428 | 2 |
| C2×#63651 | 2 |
| C2×#63649 | 2 |
| #10592703 | 2 |
| #10592698 | 2 |
| C2×#63637 | 2 |
| #10589396 | 2 |
| #70679 | 3 |