Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1550 conjugacy classes of subgroups; only the 416 normal subgroups are shown.
This group has 1550 conjugacy classes of subgroups — too many to draw. Only its 416 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×#376 | C4 |
| prime radical, cosocle | C23×D17 | C24 |
| hypercenter | #376 | #595 |
| hypocenter | C17 | #14354 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. #11762655 | C4 | semidirect |
| 13. #11762654 | C4 | semidirect |
| 15. C17×#376 | C4 | semidirect |
| 52. C42×C17 | C4⋊C4 | semidirect |
| 53. C4×Dic17 | C4⋊C4 | semidirect |
| 54. C4×Dic17 | C4⋊C4 | semidirect |
| 102. #376 | #595 | semidirect |
| 127. C17 | #14354 | semidirect |
| 149. C42 | C4⋊#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763755 | 2 |
| C2×#11763753 | 2 |
| #14543972 | 2 |
| D17×#376 | 2 |
| #14354 | 17 |