Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
444 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20274461 | C2 | semidirect |
| 3. #20272537 | C2 | semidirect |
| 5. C53×#1745 | C2 | semidirect |
| 157. #1745 | D53 | semidirect |
| 186. C53 | #7692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283082 | 2 |
| #20274461 | 2 |
| #20272537 | 2 |
| #20272535 | 2 |
| C53×#1745 | 2 |
| #7692 | 53 |