Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
626 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 132 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. #14544965 | C2 | semidirect |
| 3. #14544720 | C2 | semidirect |
| 4. #14543978 | C2 | semidirect |
| 15. #11763183 | C4 | semidirect |
| 16. #11763182 | C4 | semidirect |
| 17. #11763181 | C4 | semidirect |
| 20. C17×#492 | C4 | semidirect |
| 125. C8×C17 | #102 | semidirect |
| 126. #3622 | #102 | semidirect |
| 158. #492 | #595 | semidirect |
| 204. C17 | #9842 | semidirect |
| 278. C8 | #10587547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14544965 | 2 |
| #14544912 | 2 |
| #14544720 | 2 |
| #14543978 | 2 |
| D17×#492 | 2 |
| #9842 | 17 |