Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19149607 | C2 | semidirect |
| 3. #26011490 | C2 | semidirect |
| 4. C2×#19149596 | C2 | semidirect |
| 5. #390×C173 | C2 | semidirect |
| 8. #19149724 | C4 | semidirect |
| 13. C2×#14583810 | C22 | semidirect |
| 19. C2×C4⋊C4×C173 | C22 | semidirect |
| 21. C2×C42×C173 | C22 | semidirect |
| 58. Dic346 | C22⋊C4 | semidirect |
| 60. D692 | C22⋊C4 | semidirect |
| 112. C173 | #1792 | semidirect |
| 118. #390 | D173 | semidirect |
| 128. C2×C4⋊C4 | C2×D173 | semidirect |
| 130. C2×C42 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149724 | 2 |
| C2×#19149607 | 2 |
| #26011490 | 2 |
| C2×#19149596 | 2 |
| #390×C173 | 2 |
| #1792 | 173 |