Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
404 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 130 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. #26012361 | C2 | semidirect |
| 7. C2×#14583836 | C4 | semidirect |
| 11. #19149758 | C4 | semidirect |
| 16. #19149638 | C4 | semidirect |
| 20. C4⋊C4×D173 | C4 | semidirect |
| 23. #117×C173 | C4 | semidirect |
| 27. #14583836 | C2×C4 | semidirect |
| 33. C4×#10621924 | C2×C4 | semidirect |
| 110. C173 | #1733 | semidirect |
| 128. #117 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583836 | 2 |
| C2×#19149758 | 2 |
| #26012361 | 2 |
| #117×D173 | 2 |
| #1733 | 173 |