Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26012289 | C2 | semidirect |
| 2. C2×#19149705 | C2 | semidirect |
| 3. #26011508 | C2 | semidirect |
| 4. #26011496 | C2 | semidirect |
| 5. #26011464 | C2 | semidirect |
| 6. #26011261 | C2 | semidirect |
| 7. #535×C173 | C2 | semidirect |
| 35. C2×Dic346 | D4 | semidirect |
| 36. C2×D692 | D4 | semidirect |
| 48. #14583810 | D4 | semidirect |
| 50. C2×#13063436 | D4 | semidirect |
| 142. C173 | #2008 | semidirect |
| 146. #535 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012289 | 2 |
| C2×#19149705 | 2 |
| #26011508 | 2 |
| #26011496 | 2 |
| #26011464 | 2 |
| #26011261 | 2 |
| #535×C173 | 2 |
| #2008 | 173 |