Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
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×#6157 |
| commutator, socle | C23×C53 | C23×C4 |
| Fitting | C53×#376 | C4 |
| prime radical, cosocle | C23×D53 | C24 |
| hypercenter | #376 | #6157 |
| hypocenter | C53 | #14354 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. #16810469 | C4 | semidirect |
| 13. #16810468 | C4 | semidirect |
| 15. C53×#376 | C4 | semidirect |
| 52. C42×C53 | C4⋊C4 | semidirect |
| 53. C4×Dic53 | C4⋊C4 | semidirect |
| 54. C4×Dic53 | C4⋊C4 | semidirect |
| 107. #376 | #6157 | semidirect |
| 110. C53 | #14354 | semidirect |
| 149. C42 | C4⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811569 | 2 |
| C2×#16811567 | 2 |
| #20289903 | 2 |
| #376×D53 | 2 |
| #14354 | 53 |