Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1304 conjugacy classes of subgroups; only the 501 normal subgroups are shown.
This group has 1304 conjugacy classes of subgroups — too many to draw. Only its 501 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 | C24×D53 |
| commutator, socle, prime radical, cosocle | C23×C53 | C25 |
| Fitting | C53×#2845 | C2 |
| hypercenter | #2845 | D53 |
| hypocenter | C53 | #36701 |
| LCS | G ▷ C23×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ #2845 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 103. C53 | #36701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282965 | 2 |
| #20282783 | 2 |
| #20278019 | 2 |
| #20277270 | 2 |
| C53×#2845 | 2 |
| #36701 | 53 |