Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
480 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 165 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×#19149678 | C2 | semidirect |
| 3. #26011769 | C2 | direct (N × H) |
| 4. C2×#19149613 | C2 | semidirect |
| 5. C2×#19149612 | C2 | semidirect |
| 6. C2×#19149608 | C2 | semidirect |
| 13. #19149678 | C22 | semidirect |
| 21. #19149613 | C22 | semidirect |
| 22. #19149612 | C22 | semidirect |
| 23. #19149608 | C22 | semidirect |
| 50. C2×D4×C173 | Q8 | semidirect |
| 76. D4×C173 | C2×Q8 | semidirect |
| 101. C2×C173 | #474 | semidirect |
| 105. C173 | C2×#474 | semidirect |
| 140. C2×D4 | Dic346 | semidirect |
| 172. D4 | C2×Dic346 | semidirect |
| 207. C2 | #26011769 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149678 | 2 |
| C2×D4×Dic173 | 2 |
| #26011769 | 2 |
| C2×#19149613 | 2 |
| C2×#19149612 | 2 |
| C2×#19149608 | 2 |
| C2×#19149600 | 2 |
| C2×#102×C173 | 2 |
| C2×#474 | 173 |