Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
417 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 417 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 216. C32 | #2089 | semidirect |
| 252. C3 | #68923 | semidirect |
| 253. C3 | #70532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63645 | 2 |
| C3×#5102 | 2 |
| #10591131 | 2 |
| C3×#4552 | 2 |
| #10589168 | 2 |
| #70532 | 3 |
| #68923 | 3 |