Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1168 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 209 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. C22×#14583803 | C2 | semidirect |
| 3. C2×#19149586 | C2 | semidirect |
| 4. C2×#95×C173 | C2 | semidirect |
| 9. C22×D692 | C4 | semidirect |
| 35. C22×Dic173 | D4 | semidirect |
| 46. C22×C4×C173 | D4 | semidirect |
| 67. C22×D173 | C22⋊C4 | semidirect |
| 90. C2×C4×C173 | C22⋊C4 | semidirect |
| 128. C173 | #1438 | semidirect |
| 133. C2×#95 | D173 | semidirect |
| 174. C22×C4 | D692 | semidirect |
| 219. C2×C4 | #14583803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D692 | 2 |
| C22×#14583803 | 2 |
| C2×#19149586 | 2 |
| C2×#95×C173 | 2 |
| #1438 | 173 |