Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
444 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 2. #14544441 | C2 | semidirect |
| 4. #14543985 | C2 | semidirect |
| 5. #14543679 | C2 | semidirect |
| 6. #14543672 | C2 | semidirect |
| 8. #11763860 | C4 | semidirect |
| 9. Q8×#3624 | C4 | semidirect |
| 10. #11763843 | C4 | semidirect |
| 12. #11763837 | C4 | semidirect |
| 22. #11763666 | C4 | semidirect |
| 23. #11763665 | C4 | semidirect |
| 265. C17 | #8247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545600 | 2 |
| #14544441 | 2 |
| #14544237 | 2 |
| #14543985 | 2 |
| #14543679 | 2 |
| #14543672 | 2 |
| #14527269 | 2 |
| #8247 | 17 |