Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
318 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 14. #11763736 | C4 | semidirect |
| 15. #11763735 | C4 | semidirect |
| 16. #11763700 | C4 | semidirect |
| 17. #11763699 | C4 | semidirect |
| 23. #11762633 | C4 | semidirect |
| 24. #11762632 | C4 | semidirect |
| 25. #11762631 | C4 | semidirect |
| 26. C17×#365 | C4 | semidirect |
| 92. C16×C17 | C42 | semidirect |
| 93. #63214 | C42 | semidirect |
| 160. #365 | #595 | semidirect |
| 203. C17 | #12677 | semidirect |
| 237. C16 | C4×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545136 | 2 |
| #14544999 | 2 |
| #14544600 | 2 |
| #14544593 | 2 |
| #14543860 | 2 |
| #14543857 | 2 |
| D17×#365 | 2 |
| #12677 | 17 |