Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
616 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 1. #14544309 | C2 | semidirect |
| 4. #14544207 | C2 | semidirect |
| 5. #14544206 | C2 | semidirect |
| 6. #14544148 | C2 | semidirect |
| 23. Q8×Dic34 | C4 | semidirect |
| 25. #11763534 | C4 | semidirect |
| 28. #11763516 | C4 | semidirect |
| 38. C17×#556 | C4 | semidirect |
| 259. #556 | #595 | semidirect |
| 366. C17 | #8501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544309 | 2 |
| #14544268 | 2 |
| #14544226 | 2 |
| #14544207 | 2 |
| #14544206 | 2 |
| #14544148 | 2 |
| #14543260 | 2 |
| #8501 | 17 |