Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
718 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 211 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. #14537635 | C2 | semidirect |
| 3. #14530659 | C2 | semidirect |
| 4. #14530630 | C2 | semidirect |
| 5. #14530499 | C2 | semidirect |
| 6. #14530380 | C2 | semidirect |
| 7. C17×#2158 | C2 | semidirect |
| 10. C2×D272 | C4 | semidirect |
| 15. #11762891 | C22 | semidirect |
| 18. #11762609 | C22 | semidirect |
| 19. #11762584 | C22 | semidirect |
| 20. C16×Dic17 | C22 | semidirect |
| 23. C17×#367 | C22 | semidirect |
| 24. C17×#366 | C22 | semidirect |
| 32. C2×D136 | C2×C4 | semidirect |
| 37. C2×C16×C17 | C2×C4 | semidirect |
| 47. D272 | C2×C4 | semidirect |
| 48. D272 | C2×C4 | semidirect |
| 98. #2158 | D17 | semidirect |
| 124. #367 | C2×D17 | semidirect |
| 125. #366 | C2×D17 | semidirect |
| 149. C2×C16 | C4×D17 | semidirect |
| 157. C17 | #33456 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D272 | 2 |
| #14537635 | 2 |
| #14530659 | 2 |
| #14530630 | 2 |
| #14530499 | 2 |
| #14530380 | 2 |
| C17×#2158 | 2 |
| #33456 | 17 |