Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
564 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 123 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. #14539523 | C2 | semidirect |
| 2. #14537689 | C2 | semidirect |
| 3. #14531000 | C2 | semidirect |
| 4. #14530952 | C2 | semidirect |
| 5. #14530861 | C2 | semidirect |
| 6. #14530860 | C2 | semidirect |
| 7. #14530731 | C2 | semidirect |
| 8. #14530681 | C2 | semidirect |
| 9. #14530679 | C2 | semidirect |
| 10. #14530595 | C2 | semidirect |
| 11. C17×#2230 | C2 | semidirect |
| 17. #11763186 | C22 | semidirect |
| 27. #11762920 | C22 | semidirect |
| 31. #11762631 | C22 | semidirect |
| 32. #11762630 | C22 | semidirect |
| 33. #11762623 | C22 | semidirect |
| 34. #11762621 | C22 | semidirect |
| 37. #11762586 | C22 | semidirect |
| 38. C17×#498 | C22 | semidirect |
| 40. C17×#365 | C22 | semidirect |
| 41. C17×#364 | C22 | semidirect |
| 113. Q16×C17 | #41 | semidirect |
| 115. D8×C17 | #41 | semidirect |
| 137. Dic68 | #41 | semidirect |
| 142. D136 | #41 | semidirect |
| 202. #2230 | D17 | semidirect |
| 231. #498 | C2×D17 | semidirect |
| 248. #365 | C2×D17 | semidirect |
| 250. #364 | C2×D17 | semidirect |
| 314. C17 | #33688 | semidirect |
| 336. Q16 | #63256 | semidirect |
| 347. D8 | #63256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539523 | 2 |
| #14537689 | 2 |
| #14531000 | 2 |
| #14530952 | 2 |
| #14530861 | 2 |
| #14530860 | 2 |
| #14530731 | 2 |
| #14530681 | 2 |
| #14530679 | 2 |
| #14530595 | 2 |
| C17×#2230 | 2 |
| #33688 | 17 |