Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
318 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 104 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. #11763734 | C4 | semidirect |
| 17. #11763733 | C4 | semidirect |
| 23. #11762587 | C4 | semidirect |
| 24. #11762586 | C4 | semidirect |
| 25. #11762586 | C4 | semidirect |
| 26. C17×#347 | C4 | semidirect |
| 91. C16×C17 | C42 | semidirect |
| 93. #63214 | C42 | semidirect |
| 160. #347 | #595 | semidirect |
| 201. C17 | #12677 | semidirect |
| 235. 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 |
| D17⋊#365 | 2 |
| #14544598 | 2 |
| #14544590 | 2 |
| #14543859 | 2 |
| #14543856 | 2 |
| D17×#347 | 2 |
| #12677 | 17 |