Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 5. C22×Dic353 | C4 | semidirect |
| 9. C22⋊Dic353 | C4 | semidirect |
| 13. C22⋊C4×C353 | C4 | semidirect |
| 53. C353 | #342 | semidirect |
| 67. C22⋊C4 | Dic353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊Dic353 | 2 |
| C2×C22⋊C4×C353 | 2 |
| #342 | 353 |