Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
268 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 268 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 |
|---|---|---|
| 4. #20272777 | C2 | semidirect |
| 5. #20272775 | C2 | semidirect |
| 6. #20272754 | C2 | semidirect |
| 7. C53×#1358 | C2 | semidirect |
| 113. #1358 | D53 | semidirect |
| 134. C53 | #11990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285371 | 2 |
| #20276530 | 2 |
| #20276479 | 2 |
| #20272777 | 2 |
| #20272775 | 2 |
| #20272754 | 2 |
| C53×#1358 | 2 |
| #11990 | 53 |