Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149710 | C2 | semidirect |
| 3. #26012065 | C2 | semidirect |
| 4. #26011652 | C2 | semidirect |
| 5. #26011645 | C2 | semidirect |
| 6. #26011500 | C2 | semidirect |
| 7. #26011488 | C2 | semidirect |
| 8. #26011457 | C2 | semidirect |
| 9. C22×Q16×C173 | C2 | semidirect |
| 140. C173 | #3011 | semidirect |
| 144. C22×Q16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149727 | 2 |
| C2×#19149710 | 2 |
| #26012065 | 2 |
| #26011652 | 2 |
| #26011645 | 2 |
| #26011500 | 2 |
| #26011488 | 2 |
| #26011457 | 2 |
| C22×Q16×C173 | 2 |
| #3011 | 173 |