Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
510 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 126 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. #20290262 | C2 | semidirect |
| 2. #20290014 | C2 | semidirect |
| 3. #20289955 | C2 | semidirect |
| 4. #20289918 | C2 | semidirect |
| 54. C2×D8×C53 | C8 | semidirect |
| 173. C53 | #9668 | semidirect |
| 179. C2×D8 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290262 | 2 |
| #20290014 | 2 |
| #20289955 | 2 |
| #20289918 | 2 |
| C2×D8×Dic53 | 2 |
| #9668 | 53 |