Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
264 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26038489 | C2 | semidirect |
| 3. #26038303 | C2 | semidirect |
| 4. #26038174 | C2 | semidirect |
| 5. #26038173 | C2 | semidirect |
| 6. #26038172 | C2 | semidirect |
| 7. #327×C179 | C2 | semidirect |
| 9. #19153112 | C4 | semidirect |
| 10. #19153109 | C4 | semidirect |
| 14. D4×Dic179 | C4 | semidirect |
| 15. #19153075 | C4 | semidirect |
| 119. C179 | #1517 | semidirect |
| 127. #327 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038984 | 2 |
| #26038489 | 2 |
| #26038303 | 2 |
| #26038174 | 2 |
| #26038173 | 2 |
| #26038172 | 2 |
| #327×C179 | 2 |
| #1517 | 179 |