Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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×#14583827 | C2 | semidirect |
| 3. #26011604 | C2 | semidirect |
| 4. #26011602 | C2 | semidirect |
| 5. #26011598 | C2 | semidirect |
| 6. #26011594 | C2 | semidirect |
| 7. #26011589 | C2 | semidirect |
| 8. #26011526 | C2 | semidirect |
| 9. #26011486 | C2 | semidirect |
| 10. #97×D173 | C2 | semidirect |
| 11. #441×C173 | C2 | semidirect |
| 13. #19149702 | C4 | semidirect |
| 41. #14583827 | C2×C4 | semidirect |
| 49. #14583813 | C2×C4 | semidirect |
| 50. D1384 | C2×C4 | semidirect |
| 54. C8×D173 | C2×C4 | semidirect |
| 65. Q16×C173 | C2×C4 | semidirect |
| 114. C173 | #2943 | semidirect |
| 121. #441 | D173 | semidirect |
| 165. Q16 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149702 | 2 |
| C4×#14583827 | 2 |
| #26011604 | 2 |
| #26011602 | 2 |
| #26011598 | 2 |
| #26011594 | 2 |
| #26011589 | 2 |
| #26011526 | 2 |
| #26011486 | 2 |
| #97×D173 | 2 |
| #441×C173 | 2 |
| #2943 | 173 |