Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
443 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 443 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 312. C32 | #2070 | semidirect |
| 355. C3 | #68723 | semidirect |
| 356. C3 | #70111 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592823 | 2 |
| C2×C3×#824 | 2 |
| #10591143 | 2 |
| #10591141 | 2 |
| C2×#63560 | 2 |
| C3×C3⋊#338 | 2 |
| #70111 | 3 |
| #68723 | 3 |