Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1422 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 312 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 | C23×#595 |
| commutator, socle | C23×C17 | C23×C4 |
| Fitting | C17×#383 | C4 |
| prime radical, cosocle | C23×D17 | C24 |
| hypercenter | #383 | #595 |
| hypocenter | C17 | #14710 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. #11762677 | C4 | semidirect |
| 13. #11762676 | C4 | semidirect |
| 15. C17×#383 | C4 | semidirect |
| 50. C42×C17 | C4⋊C4 | semidirect |
| 51. C4×Dic17 | C4⋊C4 | semidirect |
| 95. #383 | #595 | semidirect |
| 120. C17 | #14710 | semidirect |
| 140. C42 | C4⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763754 | 2 |
| C2×C42×#595 | 2 |
| #14543964 | 2 |
| D17×#383 | 2 |
| #14710 | 17 |