Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20287817 | C2 | semidirect |
| 3. #20276451 | C2 | semidirect |
| 4. #20274758 | C2 | semidirect |
| 5. #20272821 | C2 | semidirect |
| 6. #20272820 | C2 | semidirect |
| 7. C53×#2145 | C2 | semidirect |
| 14. #16810878 | C4 | semidirect |
| 15. #16810873 | C4 | semidirect |
| 43. #13133157 | D4 | semidirect |
| 65. M32×C53 | D4 | semidirect |
| 179. #2145 | D53 | semidirect |
| 208. C53 | #13077 | semidirect |
| 238. M32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287817 | 2 |
| #20284373 | 2 |
| #20276451 | 2 |
| #20274758 | 2 |
| #20272821 | 2 |
| #20272820 | 2 |
| C53×#2145 | 2 |
| #13077 | 53 |