Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 10. #16810915 | C4 | semidirect |
| 11. #16810905 | C4 | semidirect |
| 191. C53 | #9308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284516 | 2 |
| #20283798 | 2 |
| #20274727 | 2 |
| #20273118 | 2 |
| #20272611 | 2 |
| #20272573 | 2 |
| C53×#1518 | 2 |
| #9308 | 53 |