Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
296 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 62 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. #26012368 | C2 | semidirect |
| 10. #19149638 | C4 | semidirect |
| 11. C22⋊C4×D173 | C4 | semidirect |
| 13. #117×C173 | C4 | semidirect |
| 70. C173 | #1828 | semidirect |
| 79. #117 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149738 | 2 |
| #26012368 | 2 |
| #26011965 | 2 |
| #1828 | 173 |