Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #26011968 | C2 | semidirect |
| 4. #26011588 | C2 | semidirect |
| 5. #26011582 | C2 | semidirect |
| 6. #26011527 | C2 | semidirect |
| 7. #26011501 | C2 | semidirect |
| 8. #26011449 | C2 | semidirect |
| 11. C2×#14583814 | C4 | semidirect |
| 16. #19149644 | C22 | semidirect |
| 23. #19149612 | C22 | semidirect |
| 24. #19149610 | C22 | semidirect |
| 25. #19149604 | C22 | semidirect |
| 26. #19149589 | C22 | semidirect |
| 27. C8×Dic173 | C22 | semidirect |
| 34. C2×Dic346 | C2×C4 | semidirect |
| 38. #14583814 | C2×C4 | semidirect |
| 39. #14583814 | C2×C4 | semidirect |
| 40. C2×#13063436 | C2×C4 | semidirect |
| 103. C173 | #2949 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583814 | 2 |
| #26011968 | 2 |
| #26011966 | 2 |
| #26011588 | 2 |
| #26011582 | 2 |
| #26011527 | 2 |
| #26011501 | 2 |
| #26011449 | 2 |
| #418×C173 | 2 |
| #2949 | 173 |