Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
338 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#16810446 | C2 | semidirect |
| 4. #20274614 | C2 | semidirect |
| 5. #20272823 | C2 | semidirect |
| 6. #20272794 | C2 | semidirect |
| 21. C53×#358 | C4 | semidirect |
| 22. C53×#357 | C4 | semidirect |
| 168. #358 | Dic53 | semidirect |
| 169. #357 | Dic53 | semidirect |
| 171. C53 | #13143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810446 | 2 |
| C2×#16810433 | 2 |
| #20275609 | 2 |
| #20274614 | 2 |
| #20272823 | 2 |
| #20272794 | 2 |
| C53×#2139 | 2 |
| #13143 | 53 |