Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
574 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20277080 | C2 | semidirect |
| 5. #20272609 | C2 | semidirect |
| 6. #20272570 | C2 | semidirect |
| 7. C53×#1491 | C2 | semidirect |
| 11. #16810918 | C4 | semidirect |
| 12. #16810823 | C4 | semidirect |
| 121. Q8×C53 | #104 | semidirect |
| 182. #1491 | D53 | semidirect |
| 212. C53 | #9326 | semidirect |
| 306. Q8 | #13133143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284837 | 2 |
| #20277080 | 2 |
| #20275634 | 2 |
| #20273224 | 2 |
| #20272609 | 2 |
| #20272570 | 2 |
| C53×#1491 | 2 |
| #9326 | 53 |