Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
478 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 29. #13133216 | C8 | semidirect |
| 187. C53 | #7588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290631 | 2 |
| #20290430 | 2 |
| #20289534 | 2 |
| #20289533 | 2 |
| C4×#13133216 | 2 |
| #7588 | 53 |