Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
588 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26011509 | C2 | semidirect |
| 3. #26011507 | C2 | semidirect |
| 4. #26011496 | C2 | semidirect |
| 5. #26011473 | C2 | semidirect |
| 6. #26011464 | C2 | semidirect |
| 7. #418×C173 | C2 | semidirect |
| 15. C2×#14583825 | C4 | semidirect |
| 18. C2×D4×D173 | C4 | semidirect |
| 19. C2×#14583810 | C22 | semidirect |
| 20. #19149638 | C22 | semidirect |
| 28. C2×M16×C173 | C22 | semidirect |
| 29. #117×C173 | C22 | semidirect |
| 153. C173 | #1795 | semidirect |
| 159. #418 | D173 | semidirect |
| 175. C2×M16 | C2×D173 | semidirect |
| 177. #117 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149724 | 2 |
| #26011509 | 2 |
| #26011507 | 2 |
| #26011496 | 2 |
| #26011473 | 2 |
| #26011464 | 2 |
| #418×C173 | 2 |
| #1795 | 173 |