Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
376 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 113 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×#19149611 | C2 | semidirect |
| 2. C2×#19149600 | C2 | semidirect |
| 3. C2×#19149589 | C2 | semidirect |
| 4. #26011394 | C2 | semidirect |
| 16. C2×D8×C173 | C4 | semidirect |
| 61. C8×C173 | C22⋊C4 | semidirect |
| 82. C173 | #1972 | semidirect |
| 92. C2×D8 | Dic173 | semidirect |
| 144. C8 | C22⋊Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149611 | 2 |
| C2×#19149600 | 2 |
| C2×#19149589 | 2 |
| #26011394 | 2 |
| C22×D8×C173 | 2 |
| #1972 | 173 |