Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
360 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 2. #20274835 | C2 | semidirect |
| 3. #20273501 | C2 | semidirect |
| 6. #20272566 | C2 | semidirect |
| 7. C53×#1300 | C2 | semidirect |
| 176. #1300 | D53 | semidirect |
| 207. C53 | #8877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283856 | 2 |
| #20274835 | 2 |
| #20273501 | 2 |
| #20273199 | 2 |
| #20273129 | 2 |
| #20272566 | 2 |
| C53×#1300 | 2 |
| #8877 | 53 |