Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
412 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 412 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. C22×#14583810 | C2 | semidirect |
| 2. C2×#19149600 | C2 | semidirect |
| 3. #26011351 | C2 | semidirect |
| 4. #26011253 | C2 | semidirect |
| 17. #121×C173 | C4 | semidirect |
| 24. C2×#13063436 | D4 | semidirect |
| 104. C173 | #1895 | semidirect |
| 118. #121 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583810 | 2 |
| C2×#19149600 | 2 |
| #26011351 | 2 |
| #26011253 | 2 |
| C2×#121×C173 | 2 |
| #1895 | 173 |