Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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×#19149636 | C2 | semidirect |
| 3. C2×C4⋊C4×D173 | C2 | semidirect |
| 4. #26011397 | C2 | semidirect |
| 5. #26011396 | C2 | semidirect |
| 6. #26011394 | C2 | semidirect |
| 7. #26011367 | C2 | semidirect |
| 8. #26011349 | C2 | semidirect |
| 9. #390×C173 | C2 | semidirect |
| 12. C2×#14583825 | C4 | semidirect |
| 36. C2×Dic346 | C2×C4 | semidirect |
| 42. C22×Dic173 | C2×C4 | semidirect |
| 61. C2×D4×C173 | C2×C4 | semidirect |
| 88. C4×D173 | C22⋊C4 | semidirect |
| 133. C173 | #2311 | semidirect |
| 141. #390 | D173 | semidirect |
| 177. C2×D4 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583825 | 2 |
| C2×#19149636 | 2 |
| C2×C4⋊C4×D173 | 2 |
| #26011397 | 2 |
| #26011396 | 2 |
| #26011394 | 2 |
| #26011367 | 2 |
| #26011349 | 2 |
| #390×C173 | 2 |
| #2311 | 173 |