Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 288 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 |
|---|---|---|
| 3. #26038177 | C2 | semidirect |
| 5. C22×Dic358 | C4 | semidirect |
| 8. #19153092 | C4 | semidirect |
| 11. C2×C4⋊Dic179 | C4 | semidirect |
| 98. C179 | #1520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153092 | 2 |
| #26038299 | 2 |
| #26038177 | 2 |
| C2×C22⋊C8×C179 | 2 |
| #1520 | 179 |