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 |
| 10. C22×C8×D17 | C4 | semidirect |
| 15. C2×C4⋊#3622 | C4 | semidirect |
| 16. C2×#10587491 | C4 | semidirect |
| 18. C2×C4×C8×C17 | C4 | semidirect |
| 98. C22×D17 | #107 | semidirect |
| 112. C2×C4×C17 | #107 | semidirect |
| 129. C8×C17 | #99 | semidirect |
| 171. C2×C4×C8 | #595 | semidirect |
| 212. C17 | #8609 | semidirect |
| 288. C2×C4 | #10587534 | semidirect |
| 295. C8 | #10587539 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544661 | 2 |
| #14544645 | 2 |
| #14543647 | 2 |
| C2×C8×D68 | 2 |
| #8609 | 17 |