Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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. #26011971 | C2 | semidirect |
| 3. #26011604 | C2 | semidirect |
| 4. #26011599 | C2 | semidirect |
| 5. C4×#14583815 | C2 | semidirect |
| 6. C2×#19149611 | C2 | semidirect |
| 7. #26011493 | C2 | semidirect |
| 8. #405×C173 | C2 | semidirect |
| 10. #19149701 | C4 | semidirect |
| 30. #14583826 | C2×C4 | semidirect |
| 37. Dic692 | C2×C4 | semidirect |
| 38. #14583815 | C2×C4 | semidirect |
| 39. D1384 | C2×C4 | semidirect |
| 47. C2×C8×C173 | C2×C4 | semidirect |
| 90. C173 | #2952 | semidirect |
| 99. #405 | D173 | semidirect |
| 133. C2×C8 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| #26011971 | 2 |
| #26011604 | 2 |
| #26011599 | 2 |
| C4×#14583815 | 2 |
| C2×#19149611 | 2 |
| #26011493 | 2 |
| #405×C173 | 2 |
| #2952 | 173 |