Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
104 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 39 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. #26015022 | C2 | semidirect |
| 3. C2×#19150726 | C2 | semidirect |
| 4. #26014928 | C2 | semidirect |
| 5. #26014910 | C2 | semidirect |
| 6. #26014908 | C2 | semidirect |
| 7. #131×C353 | C2 | semidirect |
| 51. C353 | #471 | semidirect |
| 56. #131 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26015022 | 2 |
| #26015017 | 2 |
| C2×#19150726 | 2 |
| #26014928 | 2 |
| #26014910 | 2 |
| #26014908 | 2 |
| #131×C353 | 2 |
| #471 | 353 |