Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
512 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. #26011517 | C2 | direct (N × H) |
| 4. C2×#19149608 | C2 | semidirect |
| 14. #19149608 | C22 | semidirect |
| 66. C2×C173 | #424 | semidirect |
| 69. C173 | C2×#424 | semidirect |
| 136. C2 | #26011517 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583810 | 2 |
| C2×#19149638 | 2 |
| #26011517 | 2 |
| C2×#19149608 | 2 |
| C23×C8×C173 | 2 |
| C2×#424 | 173 |