Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20287818 | C2 | semidirect |
| 2. #20276451 | C2 | semidirect |
| 3. #20274761 | C2 | semidirect |
| 4. #20272822 | C2 | semidirect |
| 16. C53×#470 | C4 | semidirect |
| 17. C53×#469 | C4 | semidirect |
| 24. #13133157 | D4 | semidirect |
| 150. #470 | Dic53 | semidirect |
| 151. #469 | Dic53 | semidirect |
| 159. C53 | #13077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287818 | 2 |
| #20276451 | 2 |
| #20274761 | 2 |
| #20272822 | 2 |
| C53×#3060 | 2 |
| #13077 | 53 |