Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
582 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 118 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. #14544523 | C2 | semidirect |
| 4. #14543625 | C2 | semidirect |
| 7. C23×#3624 | C4 | semidirect |
| 10. C2×#10587544 | C4 | semidirect |
| 13. C2×C22⋊#3624 | C4 | semidirect |
| 15. C2×C4×#3624 | C4 | semidirect |
| 21. #11762534 | C4 | semidirect |
| 22. #11762533 | C4 | semidirect |
| 23. C17×#323 | C4 | semidirect |
| 107. C23×C17 | #97 | semidirect |
| 131. C2×Dic17 | #97 | semidirect |
| 141. #3624 | #99 | semidirect |
| 189. #323 | #595 | semidirect |
| 230. C17 | #8160 | semidirect |
| 285. C23 | #10587532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763836 | 2 |
| #14544531 | 2 |
| #14544523 | 2 |
| #14543625 | 2 |
| #14527099 | 2 |
| #8160 | 17 |