Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
382 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26012065 | C2 | semidirect |
| 3. C2×#19149668 | C2 | semidirect |
| 4. C2×#19149605 | C2 | semidirect |
| 5. #26011497 | C2 | semidirect |
| 6. #26011252 | C2 | semidirect |
| 7. C2×#101×C173 | C2 | semidirect |
| 130. C173 | #2003 | semidirect |
| 137. C2×#101 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149707 | 2 |
| #26012065 | 2 |
| C2×#19149668 | 2 |
| C2×#19149605 | 2 |
| #26011497 | 2 |
| #26011252 | 2 |
| C2×#101×C173 | 2 |
| #2003 | 173 |