Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
434 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 115 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×#16810439 | C2 | semidirect |
| 4. #20276435 | C2 | semidirect |
| 5. #20276320 | C2 | semidirect |
| 6. #20274839 | C2 | semidirect |
| 24. C53×#495 | C4 | semidirect |
| 25. C53×#494 | C4 | semidirect |
| 183. #495 | Dic53 | semidirect |
| 184. #494 | Dic53 | semidirect |
| 195. C53 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810439 | 2 |
| #20276451 | 2 |
| #20276443 | 2 |
| #20276435 | 2 |
| #20276320 | 2 |
| #20274839 | 2 |
| C53×#3156 | 2 |
| #13216 | 53 |