Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
274 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 10. C8×#3624 | C4 | semidirect |
| 13. #11762630 | C4 | semidirect |
| 15. C17×#364 | C4 | semidirect |
| 24. #10587536 | C8 | semidirect |
| 26. #10587534 | C8 | semidirect |
| 109. #364 | #595 | semidirect |
| 139. C17 | #7179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544586 | 2 |
| C8×#63242 | 2 |
| D17×#364 | 2 |
| #7179 | 17 |