Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
584 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 194 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, prime radical | C23×C53 | C23×C4 |
| Fitting | C53×#382 | C4 |
| cosocle | C22×Dic53 | C24 |
| hypercenter | #382 | #6157 |
| hypocenter | C53 | #23372 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 131. C53 | #23372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290815 | 2 |
| #20290773 | 2 |
| #20290772 | 2 |
| #20290630 | 2 |
| #20277270 | 2 |
| #23372 | 53 |