Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
590 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 148 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. #20290836 | C2 | semidirect |
| 2. C2×#16811484 | C2 | semidirect |
| 3. C2×D4⋊#88324 | C2 | semidirect |
| 4. C2×#16811464 | C2 | semidirect |
| 46. C2×D8×C53 | C8 | semidirect |
| 114. C8×C53 | C22⋊C8 | semidirect |
| 161. C53 | #9659 | semidirect |
| 166. C2×D8 | #88324 | semidirect |
| 257. C8 | C22⋊#88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290836 | 2 |
| C2×#16811484 | 2 |
| C2×D4⋊#88324 | 2 |
| C2×#16811464 | 2 |
| C2×D8×Dic53 | 2 |
| #9659 | 53 |