Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
482 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 2. #14544577 | C2 | semidirect |
| 4. #14543990 | C2 | semidirect |
| 5. #14543681 | C2 | semidirect |
| 6. #14543676 | C2 | semidirect |
| 10. #11763844 | C4 | semidirect |
| 12. D4×#3624 | C4 | semidirect |
| 26. #11762556 | C4 | semidirect |
| 27. #11762554 | C4 | semidirect |
| 28. #11762553 | C4 | semidirect |
| 29. C17×#331 | C4 | semidirect |
| 200. #331 | #595 | semidirect |
| 249. C17 | #8251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545506 | 2 |
| #14544577 | 2 |
| #14544164 | 2 |
| #14543990 | 2 |
| #14543681 | 2 |
| #14543676 | 2 |
| #14527430 | 2 |
| #8251 | 17 |