Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
528 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #20275660 | C2 | semidirect |
| 4. #20273317 | C2 | semidirect |
| 6. #20272572 | C2 | semidirect |
| 7. C53×#3236 | C2 | semidirect |
| 200. #3236 | D53 | semidirect |
| 238. C53 | #10009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284810 | 2 |
| #20279882 | 2 |
| #20275660 | 2 |
| #20273317 | 2 |
| #20273157 | 2 |
| #20272572 | 2 |
| C53×#3236 | 2 |
| #10009 | 53 |