Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
234 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26014987 | C2 | semidirect |
| 2. #26014983 | C2 | semidirect |
| 3. #26014981 | C2 | semidirect |
| 4. #26014977 | C2 | semidirect |
| 5. #26014968 | C2 | semidirect |
| 7. C4×D1412 | C2 | semidirect |
| 8. C4×D1412 | C2 | semidirect |
| 9. #26014949 | C2 | semidirect |
| 10. C42×D353 | C2 | semidirect |
| 11. C4×Q8×C353 | C2 | semidirect |
| 74. C353 | #529 | semidirect |
| 82. C4×Q8 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26014987 | 2 |
| #26014983 | 2 |
| #26014981 | 2 |
| #26014977 | 2 |
| #26014968 | 2 |
| #26014967 | 2 |
| C4×D1412 | 2 |
| #26014949 | 2 |
| C42×D353 | 2 |
| C4×Q8×C353 | 2 |
| #529 | 353 |