Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 101 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. #20276488 | C2 | semidirect |
| 4. #20274602 | C2 | semidirect |
| 5. #20272818 | C2 | semidirect |
| 6. #20272798 | C2 | semidirect |
| 21. C53×#362 | C4 | semidirect |
| 22. C53×#361 | C4 | semidirect |
| 157. #362 | Dic53 | semidirect |
| 158. #361 | Dic53 | semidirect |
| 161. C53 | #13140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276488 | 2 |
| #20276451 | 2 |
| #20275609 | 2 |
| #20274602 | 2 |
| #20272818 | 2 |
| #20272798 | 2 |
| C53×#2148 | 2 |
| #13140 | 53 |