Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
550 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 108 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. #14544661 | C2 | semidirect |
| 3. #14543647 | C2 | semidirect |
| 14. C2×#10587485 | C4 | semidirect |
| 15. C2×C22⋊#3622 | C4 | semidirect |
| 17. C2×C8×Dic17 | C4 | semidirect |
| 18. C23×C8×C17 | C4 | semidirect |
| 95. C23×C17 | #107 | semidirect |
| 122. C2×Dic17 | #107 | semidirect |
| 129. C8×C17 | #99 | semidirect |
| 162. C23×C8 | #595 | semidirect |
| 212. C17 | #8609 | semidirect |
| 265. C23 | #10587534 | semidirect |
| 295. C8 | #10587551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544661 | 2 |
| #14544644 | 2 |
| #14543647 | 2 |
| C2×C8×C22⋊D17 | 2 |
| #8609 | 17 |