Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
316 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 2. #14545004 | C2 | semidirect |
| 4. #14544903 | C2 | semidirect |
| 5. #14543862 | C2 | semidirect |
| 6. #14543861 | C2 | semidirect |
| 23. #11762623 | C4 | semidirect |
| 24. #11762622 | C4 | semidirect |
| 25. #11762621 | C4 | semidirect |
| 26. C17×#361 | C4 | semidirect |
| 169. #361 | #595 | semidirect |
| 214. C17 | #13158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763727 | 2 |
| #14545004 | 2 |
| #14544945 | 2 |
| #14544903 | 2 |
| #14543862 | 2 |
| #14543861 | 2 |
| D17×#361 | 2 |
| #13158 | 17 |