Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1198 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 196 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. C2×#16811518 | C2 | semidirect |
| 2. C2×C22⋊#11719910 | C2 | semidirect |
| 4. C22×#11719910 | C22 | semidirect |
| 44. C23×D53 | C16 | semidirect |
| 123. C22×C53 | C22⋊C16 | semidirect |
| 136. C2×D53 | C22⋊C16 | semidirect |
| 162. C53 | #12679 | semidirect |
| 279. C22 | #16811518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811518 | 2 |
| C2×C22⋊#11719910 | 2 |
| C23×C8×D53 | 2 |
| #12679 | 53 |