Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
682 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20273380 | C2 | semidirect |
| 2. #20273353 | C2 | semidirect |
| 3. #20273149 | C2 | semidirect |
| 4. #20273067 | C2 | semidirect |
| 198. C53 | #8477 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20273380 | 2 |
| #20273353 | 2 |
| #20273149 | 2 |
| #20273067 | 2 |
| C53×#3510 | 2 |
| #8477 | 53 |