Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
536 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 82 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. #26012489 | C2 | semidirect |
| 2. #26012484 | C2 | semidirect |
| 3. #26012477 | C2 | semidirect |
| 4. #26012470 | C2 | semidirect |
| 20. C2×#14583825 | C4 | semidirect |
| 23. C22×Dic346 | C4 | semidirect |
| 24. C2×Q8×D173 | C4 | semidirect |
| 26. C2×#41×C173 | C4 | semidirect |
| 141. C173 | #1796 | semidirect |
| 156. C2×#41 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012489 | 2 |
| #26012484 | 2 |
| #26012477 | 2 |
| #26012470 | 2 |
| C2×#19149726 | 2 |
| #1796 | 173 |