Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
554 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20283798 | C2 | semidirect |
| 3. #20274708 | C2 | semidirect |
| 5. #20272617 | C2 | semidirect |
| 6. #20272616 | C2 | semidirect |
| 207. C53 | #9406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283798 | 2 |
| #20279718 | 2 |
| #20274708 | 2 |
| #20273383 | 2 |
| #20272617 | 2 |
| #20272616 | 2 |
| C53×#1545 | 2 |
| #9406 | 53 |