Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#19149619 | C2 | semidirect |
| 3. #26011294 | C2 | semidirect |
| 4. #26011291 | C2 | semidirect |
| 5. C2×#107×C173 | C2 | semidirect |
| 8. #19149701 | C4 | semidirect |
| 25. Dic692 | C2×C4 | semidirect |
| 28. D1384 | C2×C4 | semidirect |
| 73. C173 | #2139 | semidirect |
| 77. C2×#107 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149701 | 2 |
| C2×#19149619 | 2 |
| #26011294 | 2 |
| #26011291 | 2 |
| C2×#107×C173 | 2 |
| #2139 | 173 |