Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
346 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 59. #101×C53 | C8 | semidirect |
| 182. C53 | #9549 | semidirect |
| 204. #101 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290266 | 2 |
| #20290017 | 2 |
| C2×Q8⋊#88324 | 2 |
| M16×#88324 | 2 |
| #20289561 | 2 |
| #20289548 | 2 |
| #101×Dic53 | 2 |
| #9549 | 53 |