Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
326 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 58 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 |
|---|---|---|
| 1. #26012462 | C2 | semidirect |
| 2. #26012434 | C2 | semidirect |
| 3. #26012343 | C2 | semidirect |
| 4. #26012342 | C2 | semidirect |
| 8. #19149736 | C22 | semidirect |
| 11. (C2×#10621924)⋊C4 | C22 | semidirect |
| 13. C2×D4×D173 | C4 | semidirect |
| 16. #19149653 | C4 | semidirect |
| 20. C4⋊C4×D173 | C4 | semidirect |
| 22. #121×C173 | C4 | semidirect |
| 121. C173 | #1510 | semidirect |
| 137. #121 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012462 | 2 |
| #26012434 | 2 |
| #26012343 | 2 |
| #26012342 | 2 |
| #121×D173 | 2 |
| #1510 | 173 |