Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
508 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20277896 | C2 | semidirect |
| 2. #20273441 | C2 | semidirect |
| 4. #20272580 | C2 | semidirect |
| 16. C53×#494 | C4 | semidirect |
| 17. C53×#492 | C4 | semidirect |
| 126. #494 | Dic53 | semidirect |
| 127. #492 | Dic53 | semidirect |
| 135. C53 | #9429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277896 | 2 |
| #20273441 | 2 |
| #20273262 | 2 |
| #20272580 | 2 |
| C53×#3152 | 2 |
| #9429 | 53 |