Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
582 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 2. #20290452 | C2 | semidirect |
| 4. #20289558 | C2 | semidirect |
| 6. C22×D53⋊C8 | C4 | semidirect |
| 10. C2×#13133284 | C4 | semidirect |
| 11. C2×#13133274 | C4 | semidirect |
| 15. C2×C4×#88324 | C4 | semidirect |
| 17. #16811469 | C4 | semidirect |
| 18. #16811467 | C4 | semidirect |
| 116. C22×D53 | #97 | semidirect |
| 137. C2×Dic53 | #97 | semidirect |
| 149. #88324 | #99 | semidirect |
| 208. C53 | #8160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811650 | 2 |
| #20290452 | 2 |
| #20289953 | 2 |
| #20289558 | 2 |
| #20274502 | 2 |
| #8160 | 53 |