Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26038455 | C2 | semidirect |
| 3. #26038435 | C2 | semidirect |
| 4. #26038407 | C2 | semidirect |
| 5. #26038210 | C2 | semidirect |
| 6. #26038203 | C2 | semidirect |
| 7. #568×C179 | C2 | semidirect |
| 10. #19153143 | C4 | semidirect |
| 12. #19153138 | C4 | semidirect |
| 118. C179 | #1881 | semidirect |
| 121. #568 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039237 | 2 |
| #26038455 | 2 |
| #26038435 | 2 |
| #26038407 | 2 |
| #26038210 | 2 |
| #26038203 | 2 |
| #568×C179 | 2 |
| #1881 | 179 |