Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
258 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26011465 | C2 | semidirect |
| 3. #26011285 | C2 | semidirect |
| 4. #26011283 | C2 | semidirect |
| 5. #410×C173 | C2 | semidirect |
| 6. C2×#14583826 | C4 | semidirect |
| 7. #19149677 | C4 | semidirect |
| 9. #19149668 | C4 | semidirect |
| 16. C2×C4×Dic173 | C4 | semidirect |
| 113. C173 | #2126 | semidirect |
| 117. #410 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012037 | 2 |
| #26011465 | 2 |
| #26011285 | 2 |
| #26011283 | 2 |
| #410×C173 | 2 |
| #2126 | 173 |