Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
186 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20276596 | C2 | semidirect |
| 2. #20272919 | C2 | semidirect |
| 3. #20272899 | C2 | semidirect |
| 4. C32×Dic53 | C2 | semidirect |
| 12. C53×Q64 | C4 | semidirect |
| 13. C53×SD64 | C4 | semidirect |
| 14. C53×D32 | C4 | semidirect |
| 70. Q64 | Dic53 | semidirect |
| 71. SD64 | Dic53 | semidirect |
| 72. D32 | Dic53 | semidirect |
| 78. C53 | #13655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276596 | 2 |
| #20272919 | 2 |
| #20272899 | 2 |
| C32×Dic53 | 2 |
| C53×#2262 | 2 |
| #13655 | 53 |