Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 2. C2×#19153121 | C2 | semidirect |
| 3. C2×#19153041 | C2 | semidirect |
| 4. #26038406 | C2 | semidirect |
| 5. #26038203 | C2 | semidirect |
| 6. #26038194 | C2 | semidirect |
| 7. C2×#104×C179 | C2 | semidirect |
| 11. C2×#15668249 | C4 | semidirect |
| 12. C2×#15668247 | C4 | semidirect |
| 13. C2×#15668246 | C4 | semidirect |
| 14. C2×#15668244 | C4 | semidirect |
| 130. C179 | #1876 | semidirect |
| 135. C2×#104 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153133 | 2 |
| C2×#19153121 | 2 |
| C2×#19153041 | 2 |
| #26038406 | 2 |
| #26038203 | 2 |
| #26038194 | 2 |
| C2×#104×C179 | 2 |
| #1876 | 179 |