Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
920 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 2. #20285268 | C2 | semidirect |
| 4. #20280663 | C2 | semidirect |
| 6. #20275558 | C2 | semidirect |
| 7. #20274931 | C2 | semidirect |
| 9. C53×#1995 | C2 | semidirect |
| 190. #1995 | D53 | semidirect |
| 225. C53 | #25691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288602 | 2 |
| #20285268 | 2 |
| #20284538 | 2 |
| #20280663 | 2 |
| #20275935 | 2 |
| #20275558 | 2 |
| #20274931 | 2 |
| #20274526 | 2 |
| C53×#1995 | 2 |
| #25691 | 53 |