Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
760 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 197 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×#14583811 | C2 | semidirect |
| 2. C2×#19149676 | C2 | semidirect |
| 3. #26011867 | C2 | direct (N × H) |
| 4. C2×C4×#13063436 | C2 | semidirect |
| 5. C2×#127×C173 | C2 | semidirect |
| 9. C2×#14583811 | C22 | semidirect |
| 12. #19149676 | C22 | semidirect |
| 13. C4×#13063436 | C22 | semidirect |
| 17. #127×C173 | C22 | semidirect |
| 26. C2×#13063436 | D4 | semidirect |
| 44. #13063436 | C2×D4 | semidirect |
| 52. C2×C4×C173 | D8 | semidirect |
| 67. C4×C173 | C2×D8 | semidirect |
| 70. C2×C173 | #493 | semidirect |
| 74. C173 | C2×#493 | semidirect |
| 78. C2×#127 | D173 | semidirect |
| 91. #127 | C2×D173 | semidirect |
| 126. C2×C4 | #14583811 | semidirect |
| 142. C4 | C2×#14583811 | semidirect |
| 146. C2 | #26011867 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583811 | 2 |
| C2×#19149676 | 2 |
| #26011867 | 2 |
| C2×C4×#13063436 | 2 |
| C2×#127×C173 | 2 |
| C2×#493 | 173 |