Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
322 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 144 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 |
|---|---|---|
| 3. #14543698 | C2 | semidirect |
| 60. #3624 | M32 | semidirect |
| 108. C17 | #11402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544991 | 2 |
| C8×#63242 | 2 |
| #14543698 | 2 |
| #14530377 | 2 |
| #11402 | 17 |