Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
528 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 104 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. #20290431 | C2 | semidirect |
| 4. #20289592 | C2 | semidirect |
| 17. #16811479 | C4 | semidirect |
| 18. #16811478 | C4 | semidirect |
| 21. #16810363 | C4 | semidirect |
| 22. #16810362 | C4 | semidirect |
| 23. C53×#329 | C4 | semidirect |
| 39. #13133272 | C2×C4 | semidirect |
| 51. #13133128 | C2×C4 | semidirect |
| 54. #97×C53 | C2×C4 | semidirect |
| 193. #329 | #6157 | semidirect |
| 194. C53 | #8224 | semidirect |
| 223. #97 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #124×#6157 | 2 |
| #20290431 | 2 |
| D53⋊#329 | 2 |
| #20289592 | 2 |
| #329×D53 | 2 |
| #8224 | 53 |