Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
574 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20277080 | C2 | semidirect |
| 4. #20273162 | C2 | semidirect |
| 5. #20272607 | C2 | semidirect |
| 6. #20272572 | C2 | semidirect |
| 24. C53×#477 | C4 | semidirect |
| 25. C53×#460 | C4 | semidirect |
| 122. Q8×C53 | #104 | semidirect |
| 195. #477 | Dic53 | semidirect |
| 196. #460 | Dic53 | semidirect |
| 212. C53 | #9326 | semidirect |
| 306. Q8 | #13133144 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277080 | 2 |
| #20275635 | 2 |
| #20273223 | 2 |
| #20273162 | 2 |
| #20272607 | 2 |
| #20272572 | 2 |
| C53×#3112 | 2 |
| #9326 | 53 |