Finite Group DatabasebetaFinite Group DatabasebetaOrder 22976.
104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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. #26040045 | C2 | semidirect |
| 2. C2×#19153329 | C2 | semidirect |
| 3. #26040022 | C2 | semidirect |
| 4. #26039950 | C2 | semidirect |
| 5. #26039933 | C2 | semidirect |
| 6. #26039932 | C2 | semidirect |
| 51. C359 | #471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26040045 | 2 |
| C2×#19153329 | 2 |
| #26040022 | 2 |
| #26039950 | 2 |
| #26039933 | 2 |
| #26039932 | 2 |
| AGL(1,ℤ/8)×C359 | 2 |
| #471 | 359 |