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 |
| 10. C22×C8×D53 | C4 | semidirect |
| 15. C2×C4⋊#88322 | C4 | semidirect |
| 16. C2×#13133129 | C4 | semidirect |
| 18. C2×C4×C8×C53 | C4 | semidirect |
| 96. C22×D53 | #106 | semidirect |
| 109. C2×C4×C53 | #106 | semidirect |
| 125. C8×C53 | #99 | semidirect |
| 173. C2×C4×C8 | #6157 | semidirect |
| 177. C53 | #8608 | semidirect |
| 279. C2×C4 | #13133285 | semidirect |
| 286. C8 | #13133276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290591 | 2 |
| #20290576 | 2 |
| #20289578 | 2 |
| C2×C8×D212 | 2 |
| #8608 | 53 |