Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
578 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26011966 | C2 | semidirect |
| 3. #26011346 | C2 | semidirect |
| 4. #26011257 | C2 | semidirect |
| 5. C2×#99×C173 | C2 | semidirect |
| 9. #19149647 | C4 | semidirect |
| 25. C23×D173 | C2×C4 | semidirect |
| 30. C22×Dic173 | D4 | semidirect |
| 36. C22⋊Dic173 | C2×C4 | semidirect |
| 72. C23×C173 | C22⋊C4 | semidirect |
| 84. C2×C4×C173 | C22⋊C4 | semidirect |
| 119. C173 | #1889 | semidirect |
| 123. C2×#99 | D173 | semidirect |
| 186. C23 | #14583803 | semidirect |
| 204. C2×C4 | #14583803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149647 | 2 |
| #26011966 | 2 |
| #26011346 | 2 |
| #26011257 | 2 |
| C2×#99×C173 | 2 |
| #1889 | 173 |