Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
560 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20284750 | C2 | semidirect |
| 4. #20273143 | C2 | semidirect |
| 6. #20272544 | C2 | semidirect |
| 7. C53×#1995 | C2 | semidirect |
| 204. #1995 | D53 | semidirect |
| 238. C53 | #10016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284750 | 2 |
| #20284719 | 2 |
| #20278001 | 2 |
| #20273143 | 2 |
| #20273139 | 2 |
| #20272544 | 2 |
| C53×#1995 | 2 |
| #10016 | 53 |