Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
184 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C2×#19149625 | C2 | semidirect |
| 2. C2×#19149623 | C2 | semidirect |
| 3. C2×#19149622 | C2 | semidirect |
| 5. #26011875 | C2 | semidirect |
| 6. C4×#14583801 | C2 | semidirect |
| 7. #495×C173 | C2 | semidirect |
| 75. C173 | #2249 | semidirect |
| 82. #495 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149625 | 2 |
| C2×#19149623 | 2 |
| C2×#19149622 | 2 |
| C2×#19149620 | 2 |
| #26011875 | 2 |
| C4×#14583801 | 2 |
| #495×C173 | 2 |
| #2249 | 173 |