Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
440 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26011455 | C2 | semidirect |
| 3. #26011214 | C2 | semidirect |
| 4. #407×C173 | C2 | semidirect |
| 15. C22⋊#13063436 | C22 | semidirect |
| 19. C22⋊C8×C173 | C22 | semidirect |
| 57. C22×D173 | M16 | semidirect |
| 110. C173 | #1462 | semidirect |
| 114. #407 | D173 | semidirect |
| 130. C22⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583803 | 2 |
| #26011455 | 2 |
| #26011214 | 2 |
| #407×C173 | 2 |
| #1462 | 173 |