Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
442 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 74 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. #20291606 | C2 | semidirect |
| 2. #20290235 | C2 | semidirect |
| 3. #20290204 | C2 | semidirect |
| 4. #20290021 | C2 | semidirect |
| 5. #20289579 | C2 | semidirect |
| 6. #20289571 | C2 | semidirect |
| 253. C53 | #9371 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291606 | 2 |
| #20290235 | 2 |
| #20290204 | 2 |
| #20290021 | 2 |
| #20289579 | 2 |
| #20289571 | 2 |
| #20285705 | 2 |
| #9371 | 53 |