Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
626 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 186 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. #20290812 | C2 | semidirect |
| 3. #20290771 | 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 |
|---|---|
| #20290812 | 2 |
| #20290784 | 2 |
| #20290771 | 2 |
| #20290662 | 2 |
| #20290649 | 2 |
| #20290644 | 2 |
| #20278017 | 2 |
| #23381 | 53 |