Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
846 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 1. #14544511 | C2 | semidirect |
| 2. #14544511 | C2 | semidirect |
| 3. C2×#11763666 | C2 | semidirect |
| 4. C2×#11763664 | C2 | semidirect |
| 308. C17 | #8336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544511 | 2 |
| C2×#11763666 | 2 |
| C2×#11763664 | 2 |
| C2×#11763341 | 2 |
| #8336 | 17 |