Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
614 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 3. #14544519 | C2 | semidirect |
| 4. #14543625 | C2 | semidirect |
| 6. C22×#63242 | C4 | semidirect |
| 10. C2×C4⋊#3624 | C4 | semidirect |
| 12. C2×#10587543 | C4 | semidirect |
| 14. C2×C4×#3624 | C4 | semidirect |
| 21. #11762535 | C4 | semidirect |
| 22. #11762532 | C4 | semidirect |
| 23. C17×#324 | C4 | semidirect |
| 52. #10587539 | C8 | semidirect |
| 77. C22⋊#595 | C2×C8 | semidirect |
| 110. C22×D17 | C4×C8 | semidirect |
| 122. C2×C4×C17 | C4×C8 | semidirect |
| 141. #3624 | #99 | semidirect |
| 188. #324 | #595 | semidirect |
| 230. C17 | C8×#99 | semidirect |
| 308. C2×C4 | C8×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763837 | 2 |
| #14544529 | 2 |
| #14544519 | 2 |
| #14543625 | 2 |
| #14527101 | 2 |
| C8×#99 | 17 |