Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
272 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 74 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×D173⋊C16 | C2 | semidirect |
| 2. C2×#19149748 | C2 | semidirect |
| 3. #26012403 | C2 | direct (N × H) |
| 7. D173⋊C16 | C22 | semidirect |
| 10. #19149748 | C22 | semidirect |
| 12. C2×D1384 | C4 | semidirect |
| 16. D8×D173 | C4 | semidirect |
| 19. C2×D8×C173 | C4 | semidirect |
| 33. D1384 | C2×C4 | semidirect |
| 43. D8×C173 | C2×C4 | semidirect |
| 88. C2×C173 | #357 | semidirect |
| 91. D173 | #357 | semidirect |
| 94. C173 | C2×#357 | semidirect |
| 107. C2×D8 | #10621924 | semidirect |
| 130. D8 | C2×#10621924 | semidirect |
| 187. C2 | #26012403 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D173⋊C16 | 2 |
| C2×#19149748 | 2 |
| #26012403 | 2 |
| C2×D8×D173 | 2 |
| C2×#357 | 173 |