Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
464 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 83 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. #14530393 | C2 | semidirect |
| 3. #14528808 | C2 | semidirect |
| 4. #14526794 | C2 | semidirect |
| 5. #14526793 | C2 | semidirect |
| 6. #14526792 | C2 | semidirect |
| 7. C17×#1347 | C2 | semidirect |
| 8. C2×D8×D17 | C4 | semidirect |
| 12. #11763046 | C4 | semidirect |
| 16. #11763042 | C4 | semidirect |
| 17. #107×D17 | C4 | semidirect |
| 21. C22⋊#63214 | C22 | semidirect |
| 23. #11762572 | C22 | semidirect |
| 25. C17×C22⋊C16 | C22 | semidirect |
| 26. C17×#340 | C22 | semidirect |
| 171. #1347 | D17 | semidirect |
| 217. C22⋊C16 | C2×D17 | semidirect |
| 219. #340 | C2×D17 | semidirect |
| 266. C17 | #11888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17×#466 | 2 |
| #14530393 | 2 |
| #14528808 | 2 |
| #14526794 | 2 |
| #14526793 | 2 |
| #14526792 | 2 |
| C17×#1347 | 2 |
| #11888 | 17 |