Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
3550 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 579 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D17 |
| commutator, socle, cosocle | C23×C17 | C25 |
| Fitting | C17×#2840 | C2 |
| prime radical | C25×D17 | C22 |
| hypercenter | #2840 | D17 |
| hypocenter | C17 | C2×#2840 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #2840 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14537037 | C2 | semidirect |
| 2. #14537036 | C2 | semidirect |
| 3. D17×#393 | C2 | semidirect |
| 5. C17×#2840 | C2 | semidirect |
| 7. C22×Q8×D17 | C22 | semidirect |
| 9. #11762722 | C22 | semidirect |
| 10. #11762721 | C22 | semidirect |
| 11. #11762720 | C22 | semidirect |
| 14. #95×D17 | C22 | semidirect |
| 15. C17×#393 | C22 | semidirect |
| 19. C24×D17 | Q8 | semidirect |
| 22. C22×Q8×C17 | C23 | semidirect |
| 25. C22×Dic34 | C23 | semidirect |
| 30. C17×#95 | C23 | semidirect |
| 31. #10587502 | C23 | semidirect |
| 33. C24×C17 | C2×Q8 | semidirect |
| 40. C23×D17 | C2×Q8 | semidirect |
| 74. #2840 | D17 | direct (N × H) |
| 96. #393 | C2×D17 | semidirect |
| 105. D17 | #2840 | direct (N × H) |
| 113. C22×Q8 | C22×D17 | semidirect |
| 120. #95 | C22×D17 | semidirect |
| 121. C17 | C2×#2840 | semidirect |
| 131. C24 | Q8×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14537037 | 2 |
| #14537036 | 2 |
| D17×#393 | 2 |
| D17×#379 | 2 |
| C17×#2840 | 2 |
| C2×#2840 | 17 |