Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1198 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 275 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×C22⋊#11719908 | C2 | semidirect |
| 3. C22×#11719908 | C22 | semidirect |
| 24. C24×C53 | C16 | semidirect |
| 67. C22×C53 | C22⋊C16 | semidirect |
| 86. C53 | #12679 | semidirect |
| 102. C24 | #11719908 | semidirect |
| 144. C22 | C22⋊#11719908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11719908 | 2 |
| C24×C8×C53 | 2 |
| #12679 | 53 |