Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
406 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 8. #11763860 | C4 | semidirect |
| 11. Q8×#3624 | C4 | semidirect |
| 26. #11762558 | C4 | semidirect |
| 27. #11762556 | C4 | semidirect |
| 28. #11762554 | C4 | semidirect |
| 29. C17×#333 | C4 | semidirect |
| 180. #333 | #595 | semidirect |
| 228. C17 | #8258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545573 | 2 |
| #14544577 | 2 |
| #14544168 | 2 |
| #14544000 | 2 |
| #14543681 | 2 |
| #14543676 | 2 |
| #14527438 | 2 |
| #8258 | 17 |