Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
550 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 106 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. #20290592 | C2 | semidirect |
| 3. #20289578 | C2 | semidirect |
| 10. C22×C8×D53 | C4 | semidirect |
| 15. C2×#13133129 | C4 | semidirect |
| 17. C2×C4×#88322 | C4 | semidirect |
| 18. C2×C4⋊C8×C53 | C4 | semidirect |
| 97. C22×D53 | #107 | semidirect |
| 111. C2×C4×C53 | #107 | semidirect |
| 130. #88322 | #99 | semidirect |
| 175. C2×C4⋊C8 | #6157 | semidirect |
| 183. C53 | #8609 | semidirect |
| 288. C2×C4 | #13133286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290592 | 2 |
| #20290576 | 2 |
| #20289578 | 2 |
| C2×#16810688 | 2 |
| #8609 | 53 |