Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 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. #26012257 | C2 | semidirect |
| 3. #26011614 | C2 | semidirect |
| 4. #26011609 | C2 | semidirect |
| 5. #26011540 | C2 | semidirect |
| 6. C2×#19149607 | C2 | semidirect |
| 7. C4×M16×C173 | C2 | semidirect |
| 9. #19149712 | C4 | semidirect |
| 10. #19149707 | C4 | semidirect |
| 13. #19149685 | C22 | semidirect |
| 16. #19149615 | C22 | semidirect |
| 17. #19149607 | C22 | semidirect |
| 18. #19149607 | C22 | semidirect |
| 22. #97×C173 | C22 | semidirect |
| 23. C4×C8×C173 | C22 | semidirect |
| 32. Dic692 | C2×C4 | semidirect |
| 33. #14583815 | C2×C4 | semidirect |
| 34. D1384 | C2×C4 | semidirect |
| 85. C173 | #2956 | semidirect |
| 93. C4×M16 | D173 | semidirect |
| 108. #97 | C2×D173 | semidirect |
| 109. 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 |
| #26012257 | 2 |
| #26011614 | 2 |
| #26011609 | 2 |
| #26011540 | 2 |
| C2×#19149607 | 2 |
| C4×M16×C173 | 2 |
| #2956 | 173 |