Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
444 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 93 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×#14583815 | C2 | semidirect |
| 2. C2×#19149659 | C2 | semidirect |
| 4. C2×#19149602 | C2 | semidirect |
| 5. C2×#19149599 | C2 | semidirect |
| 6. C2×#19149591 | C2 | semidirect |
| 7. #340×C173 | C2 | semidirect |
| 36. C2×Dic346 | D4 | semidirect |
| 66. C2×C8×C173 | D4 | semidirect |
| 70. C4⋊C4×C173 | D4 | semidirect |
| 84. C22×D173 | SD16 | semidirect |
| 157. C173 | #2000 | semidirect |
| 165. #340 | D173 | semidirect |
| 221. C2×C8 | D692 | semidirect |
| 226. C4⋊C4 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583815 | 2 |
| C2×#19149659 | 2 |
| C2×#19149654 | 2 |
| C2×#19149602 | 2 |
| C2×#19149599 | 2 |
| C2×#19149591 | 2 |
| #340×C173 | 2 |
| #2000 | 173 |