Finite Group DatabasebetaFinite Group DatabasebetaOrder 22976.
120 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 120 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. C2×#19153329 | C2 | semidirect |
| 2. C2×#19153324 | C2 | semidirect |
| 3. #26039995 | C2 | semidirect |
| 5. #26039948 | C2 | semidirect |
| 6. #26039940 | C2 | semidirect |
| 7. #102×C359 | C2 | semidirect |
| 30. C359⋊C8 | D4 | semidirect |
| 55. C359 | #468 | semidirect |
| 63. #102 | D359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153329 | 2 |
| C2×#19153324 | 2 |
| #26039995 | 2 |
| #26039986 | 2 |
| #26039948 | 2 |
| #26039940 | 2 |
| #102×C359 | 2 |
| #468 | 359 |