Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
348 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 70 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. #14545155 | C2 | semidirect |
| 2. #14544004 | C2 | semidirect |
| 3. #14543749 | C2 | semidirect |
| 4. #14543748 | C2 | semidirect |
| 5. #14543747 | C2 | semidirect |
| 6. #14543746 | C2 | semidirect |
| 9. #11763731 | C22 | semidirect |
| 10. #11763731 | C22 | semidirect |
| 14. #11763650 | C22 | semidirect |
| 15. C8×#3624 | C22 | semidirect |
| 229. C17 | #11670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545155 | 2 |
| #14544004 | 2 |
| #14543749 | 2 |
| #14543748 | 2 |
| #14543747 | 2 |
| #14543746 | 2 |
| #14537692 | 2 |
| #11670 | 17 |