Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
626 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 180 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. #20290814 | C2 | semidirect |
| 3. #20290770 | C2 | semidirect |
| 5. #20290649 | C2 | semidirect |
| 6. #20290644 | C2 | semidirect |
| 140. C53 | #23381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290814 | 2 |
| #20290787 | 2 |
| #20290770 | 2 |
| #20290663 | 2 |
| #20290649 | 2 |
| #20290644 | 2 |
| #20278018 | 2 |
| #23381 | 53 |