Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
550 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20290591 | C2 | semidirect |
| 3. #20289578 | C2 | semidirect |
| 14. C2×#13133146 | C4 | semidirect |
| 15. C2×C22⋊#88322 | C4 | semidirect |
| 17. C2×C8×Dic53 | C4 | semidirect |
| 18. C23×C8×C53 | C4 | semidirect |
| 93. C23×C53 | #106 | semidirect |
| 118. C2×Dic53 | #106 | semidirect |
| 125. C8×C53 | #99 | semidirect |
| 164. C23×C8 | #6157 | semidirect |
| 177. C53 | #8608 | semidirect |
| 257. C23 | #13133285 | semidirect |
| 286. C8 | #13133275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290591 | 2 |
| #20290575 | 2 |
| #20289578 | 2 |
| C2×C8×C22⋊D53 | 2 |
| #8608 | 53 |