Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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. #26011932 | C2 | semidirect |
| 3. C2×#19149622 | C2 | semidirect |
| 4. #26011303 | C2 | semidirect |
| 5. #26011297 | C2 | semidirect |
| 6. #26011275 | C2 | semidirect |
| 7. #473×C173 | C2 | semidirect |
| 18. #19149619 | C22 | semidirect |
| 19. C2×#14583801 | C22 | semidirect |
| 21. C2×Q16×C173 | C22 | semidirect |
| 23. #108×C173 | C22 | semidirect |
| 91. C173 | #2194 | semidirect |
| 96. #473 | D173 | semidirect |
| 106. C2×Q16 | C2×D173 | semidirect |
| 115. #108 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012296 | 2 |
| #26011932 | 2 |
| C2×#19149622 | 2 |
| #26011303 | 2 |
| #26011297 | 2 |
| #26011275 | 2 |
| #473×C173 | 2 |
| #2194 | 173 |