Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 2. C2×#19149622 | C2 | semidirect |
| 3. #26011729 | C2 | semidirect |
| 4. #26011293 | C2 | semidirect |
| 5. #26011292 | C2 | semidirect |
| 6. #26011270 | C2 | semidirect |
| 7. C2×SD32×C173 | C2 | semidirect |
| 16. C2×#14583801 | C22 | semidirect |
| 17. #19149613 | C22 | semidirect |
| 19. C2×Q16×C173 | C22 | semidirect |
| 22. C2×C16×C173 | C22 | semidirect |
| 79. C2×D173 | SD32 | semidirect |
| 91. C173 | #2187 | semidirect |
| 95. C2×SD32 | D173 | semidirect |
| 101. C2×Q16 | C2×D173 | semidirect |
| 112. C2×C16 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D173 | 2 |
| C2×#19149622 | 2 |
| #26011729 | 2 |
| #26011293 | 2 |
| #26011292 | 2 |
| #26011270 | 2 |
| C2×SD32×C173 | 2 |
| #2187 | 173 |