Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
518 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×#6157 |
| commutator, socle | C22×C53 | C43 |
| Fitting | C82×C53 | C4 |
| prime radical | C22×D53 | C2×C42 |
| cosocle | C42×D53 | C23 |
| hypercenter | C82 | #6157 |
| hypocenter | C53 | #7844 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C42 ◁ C82 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. #88324⋊C8 | C4 | semidirect |
| 12. #16811464 | C4 | semidirect |
| 15. C8×#88322 | C4 | semidirect |
| 16. C8×#88322 | C4 | semidirect |
| 17. C82×C53 | C4 | semidirect |
| 96. C82 | #6157 | semidirect |
| 97. C53 | #7844 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290428 | 2 |
| C4×#13133271 | 2 |
| #20289911 | 2 |
| #20289909 | 2 |
| C82×D53 | 2 |
| #7844 | 53 |