Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26011515 | C2 | semidirect |
| 3. C2×#19149607 | C2 | semidirect |
| 4. C43×C173 | C2 | semidirect |
| 7. #19149679 | C4 | semidirect |
| 8. #19149676 | C4 | semidirect |
| 9. #19149667 | C4 | semidirect |
| 36. C42×C173 | D4 | semidirect |
| 63. C4×C173 | #104 | semidirect |
| 72. C173 | #1962 | semidirect |
| 77. C43 | D173 | semidirect |
| 109. C42 | D692 | semidirect |
| 137. C4 | #19149607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| #26011515 | 2 |
| C2×#19149607 | 2 |
| C43×C173 | 2 |
| #1962 | 173 |