Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1462 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 1462 conjugacy classes of subgroups — too many to draw. Only its 331 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D53 |
| commutator | C23×C53 | C23×C4 |
| Fitting | C53×#1446 | C2 |
| socle, prime radical, cosocle | C24×C53 | C24 |
| hypercenter | #1446 | D53 |
| hypocenter | C53 | #14663 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ #1446 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C2×#13133215 | C4 | semidirect |
| 154. C53 | #14663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133215 | 2 |
| C2×#16810490 | 2 |
| #20272986 | 2 |
| #20272985 | 2 |
| #20272981 | 2 |
| C53×#1446 | 2 |
| #14663 | 53 |