Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1082 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 163 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. #14543189 | C2 | semidirect |
| 2. #14540162 | C2 | semidirect |
| 3. #14527927 | C2 | semidirect |
| 4. #14527898 | C2 | semidirect |
| 5. #14527865 | C2 | semidirect |
| 6. #14527836 | C2 | semidirect |
| 7. #14527519 | C2 | semidirect |
| 8. #14527236 | C2 | semidirect |
| 9. C17×#3147 | C2 | semidirect |
| 19. #11763096 | C22 | semidirect |
| 22. #11763001 | C22 | semidirect |
| 23. #11762833 | C22 | semidirect |
| 24. #11762558 | C22 | semidirect |
| 26. #11762538 | C22 | semidirect |
| 27. #11762538 | C22 | semidirect |
| 30. C17×#532 | C22 | semidirect |
| 32. C17×#494 | C22 | semidirect |
| 35. C17×#492 | C22 | semidirect |
| 36. C2×C4×C8×C17 | C22 | semidirect |
| 183. #3147 | D17 | semidirect |
| 219. #532 | C2×D17 | semidirect |
| 221. #494 | C2×D17 | semidirect |
| 224. #492 | C2×D17 | semidirect |
| 231. C2×C4×C8 | C2×D17 | semidirect |
| 292. C17 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14543189 | 2 |
| #14540162 | 2 |
| #14527927 | 2 |
| #14527898 | 2 |
| #14527865 | 2 |
| #14527836 | 2 |
| #14527519 | 2 |
| #14527236 | 2 |
| C17×#3147 | 2 |
| #18686 | 17 |