Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 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. C4×#14583826 | C2 | semidirect |
| 3. #26011604 | C2 | semidirect |
| 4. #26011599 | C2 | semidirect |
| 5. #26011593 | C2 | semidirect |
| 6. #26011529 | C2 | semidirect |
| 7. #26011488 | C2 | semidirect |
| 8. C2×#97×C173 | C2 | semidirect |
| 10. #19149701 | C4 | semidirect |
| 30. #14583826 | C2×C4 | semidirect |
| 36. Dic692 | C2×C4 | semidirect |
| 37. #14583815 | C2×C4 | semidirect |
| 38. D1384 | C2×C4 | semidirect |
| 48. C2×C8×C173 | C2×C4 | semidirect |
| 89. C173 | #2943 | semidirect |
| 98. C2×#97 | D173 | semidirect |
| 132. 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 |
| C4×#14583826 | 2 |
| #26011604 | 2 |
| #26011599 | 2 |
| #26011593 | 2 |
| #26011529 | 2 |
| #26011488 | 2 |
| C2×#97×C173 | 2 |
| #2943 | 173 |