Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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×#19150722 | C2 | semidirect |
| 2. C22×#15667725 | C2 | semidirect |
| 3. #26014966 | C2 | semidirect |
| 4. #26014925 | C2 | semidirect |
| 5. #26014913 | C2 | semidirect |
| 6. #26014912 | C2 | semidirect |
| 7. #121×C353 | C2 | semidirect |
| 27. #15667725 | D4 | semidirect |
| 43. C22×C353 | D8 | semidirect |
| 59. C353 | #466 | semidirect |
| 64. #121 | D353 | semidirect |
| 106. C22 | #19150722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150722 | 2 |
| C22×#15667725 | 2 |
| #26014966 | 2 |
| #26014925 | 2 |
| #26014913 | 2 |
| #26014912 | 2 |
| #121×C353 | 2 |
| #466 | 353 |