Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
438 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 15. #11762531 | C4 | semidirect |
| 16. #11762530 | C4 | semidirect |
| 17. C17×#322 | C4 | semidirect |
| 78. C8×C17 | #107 | semidirect |
| 80. #3622 | #107 | semidirect |
| 109. #322 | #595 | semidirect |
| 134. C17 | #8820 | semidirect |
| 177. C8 | #10587534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544720 | 2 |
| #14544719 | 2 |
| #14544705 | 2 |
| D17×#322 | 2 |
| #8820 | 17 |