Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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. #16810905 | C4 | semidirect |
| 11. #16810830 | C4 | semidirect |
| 198. C53 | #9328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284841 | 2 |
| #20277367 | 2 |
| #20275660 | 2 |
| #20273161 | 2 |
| #20272608 | 2 |
| #20272570 | 2 |
| C53×#1506 | 2 |
| #9328 | 53 |