Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20278023 | C2 | semidirect |
| 5. #20272616 | C2 | semidirect |
| 6. #20272543 | C2 | semidirect |
| 7. C53×#1303 | C2 | semidirect |
| 188. #1303 | D53 | semidirect |
| 215. C53 | #10372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20278023 | 2 |
| #20275546 | 2 |
| #20273211 | 2 |
| #20273209 | 2 |
| #20272616 | 2 |
| #20272543 | 2 |
| C53×#1303 | 2 |
| #10372 | 53 |