Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
262 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 66 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. #26012506 | C2 | semidirect |
| 3. #26012495 | C2 | semidirect |
| 5. #26012374 | C2 | semidirect |
| 6. #26012362 | C2 | semidirect |
| 25. #19149607 | C4 | semidirect |
| 26. #19149606 | C4 | semidirect |
| 27. #19149605 | C4 | semidirect |
| 28. #104×C173 | C4 | semidirect |
| 120. C173 | #1861 | semidirect |
| 149. #104 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012570 | 2 |
| #26012506 | 2 |
| #26012495 | 2 |
| #26012488 | 2 |
| #26012374 | 2 |
| #26012362 | 2 |
| #104×D173 | 2 |
| #1861 | 173 |