Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×#19149749 | C2 | semidirect |
| 3. #26012498 | C2 | semidirect |
| 5. #26012361 | C2 | semidirect |
| 6. (C2×#10621924)⋊C8 | C2 | semidirect |
| 23. #19149603 | C4 | semidirect |
| 24. #19149601 | C4 | semidirect |
| 25. #19149599 | C4 | semidirect |
| 26. #103×C173 | C4 | semidirect |
| 109. C173 | #1866 | semidirect |
| 134. #103 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149767 | 2 |
| C2×#19149749 | 2 |
| #26012498 | 2 |
| C2×#19149744 | 2 |
| #26012361 | 2 |
| (C2×#10621924)⋊C8 | 2 |
| #26011486 | 2 |
| #1866 | 173 |