Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
456 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. #14543773 | C2 | semidirect |
| 4. #14543772 | C2 | semidirect |
| 12. C2×Q16×D17 | C4 | semidirect |
| 16. #11763050 | C4 | semidirect |
| 20. #107×D17 | C4 | semidirect |
| 22. C17×#467 | C4 | semidirect |
| 179. #467 | #595 | semidirect |
| 228. C17 | #11706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545012 | 2 |
| #14544470 | 2 |
| #14543773 | 2 |
| #14543772 | 2 |
| D17×#467 | 2 |
| #11706 | 17 |