Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
482 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20276297 | C2 | semidirect |
| 3. #20276180 | C2 | semidirect |
| 4. #20276115 | C2 | semidirect |
| 6. #20275984 | C2 | semidirect |
| 171. C53 | #32872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276297 | 2 |
| #20276268 | 2 |
| #20276180 | 2 |
| #20276115 | 2 |
| #20275995 | 2 |
| #20275984 | 2 |
| #20275836 | 2 |
| #20275188 | 2 |
| C53×#1858 | 2 |
| #32872 | 53 |