Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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×#19149604 | C2 | semidirect |
| 3. C2×#19149602 | C2 | semidirect |
| 4. C2×#19149600 | C2 | semidirect |
| 5. C2×#19149591 | C2 | semidirect |
| 6. #26011348 | C2 | semidirect |
| 7. C2×#102×C173 | C2 | semidirect |
| 13. C2×#14583825 | C4 | semidirect |
| 86. Dic346 | C22⋊C4 | semidirect |
| 114. D4×C173 | C22⋊C4 | semidirect |
| 163. C173 | #1788 | semidirect |
| 169. C2×#102 | D173 | semidirect |
| 263. D4 | #14583803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583825 | 2 |
| C2×#19149604 | 2 |
| C2×#19149602 | 2 |
| C2×#19149600 | 2 |
| C2×#19149591 | 2 |
| #26011348 | 2 |
| C2×#102×C173 | 2 |
| #1788 | 173 |