Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
456 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 185 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×#19149685 | C2 | semidirect |
| 3. #26011614 | C2 | semidirect |
| 4. #26011609 | C2 | semidirect |
| 5. #26011540 | C2 | semidirect |
| 6. #26011509 | C2 | semidirect |
| 7. #405×C173 | C2 | semidirect |
| 9. #19149712 | C4 | semidirect |
| 10. #19149707 | C4 | semidirect |
| 14. #19149685 | C22 | semidirect |
| 15. #19149685 | C22 | semidirect |
| 19. #19149615 | C22 | semidirect |
| 20. #19149607 | C22 | semidirect |
| 24. #97×C173 | C22 | semidirect |
| 25. C4×C8×C173 | C22 | semidirect |
| 89. C173 | #2955 | semidirect |
| 97. #405 | D173 | semidirect |
| 114. #97 | C2×D173 | semidirect |
| 115. C4×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012291 | 2 |
| C2×#19149685 | 2 |
| #26011614 | 2 |
| #26011609 | 2 |
| #26011540 | 2 |
| #26011509 | 2 |
| #405×C173 | 2 |
| #2955 | 173 |