Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 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×#19149605 | C2 | semidirect |
| 3. #26011490 | C2 | semidirect |
| 4. C2×#19149595 | C2 | semidirect |
| 5. #26011392 | C2 | semidirect |
| 6. #26011250 | C2 | semidirect |
| 7. #428×C173 | C2 | semidirect |
| 56. M16×C173 | D4 | semidirect |
| 130. C173 | #2037 | semidirect |
| 133. #428 | D173 | semidirect |
| 181. M16 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012060 | 2 |
| C2×#19149605 | 2 |
| #26011490 | 2 |
| C2×#19149595 | 2 |
| #26011392 | 2 |
| #26011250 | 2 |
| #428×C173 | 2 |
| #2037 | 173 |