Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
331 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 331 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 275. C32 | #1593 | semidirect |
| 314. C3 | #68089 | semidirect |
| 315. C3 | #68227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#3719 | 2 |
| #10590296 | 2 |
| #10590258 | 2 |
| #10589322 | 2 |
| C3×#4456 | 2 |
| C3×#4454 | 2 |
| #10589097 | 2 |
| #68227 | 3 |
| #68089 | 3 |