Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
574 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. #20273162 | C2 | semidirect |
| 5. #20272608 | C2 | semidirect |
| 6. #20272571 | C2 | semidirect |
| 7. C53×#2276 | C2 | semidirect |
| 10. #16810918 | C4 | semidirect |
| 11. #16810823 | C4 | semidirect |
| 121. Q8×C53 | #104 | semidirect |
| 179. #2276 | D53 | semidirect |
| 212. C53 | #9326 | semidirect |
| 306. Q8 | #13133145 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284837 | 2 |
| #20275633 | 2 |
| #20273222 | 2 |
| #20273162 | 2 |
| #20272608 | 2 |
| #20272571 | 2 |
| C53×#2276 | 2 |
| #9326 | 53 |