Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
272 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20272750 | C2 | semidirect |
| 5. #20272749 | C2 | semidirect |
| 6. #20272749 | C2 | semidirect |
| 7. C53×#1356 | C2 | semidirect |
| 134. #1356 | D53 | semidirect |
| 157. C53 | #11914 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285373 | 2 |
| #20276529 | 2 |
| #20276318 | 2 |
| #20272750 | 2 |
| #20272749 | 2 |
| C53×#1356 | 2 |
| #11914 | 53 |