Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26011959 | C2 | semidirect |
| 3. #26011509 | C2 | semidirect |
| 4. C2×#19149606 | C2 | semidirect |
| 5. #26011261 | C2 | semidirect |
| 6. #26011250 | C2 | semidirect |
| 7. #410×C173 | C2 | semidirect |
| 9. #19149710 | C4 | semidirect |
| 11. #19149705 | C4 | semidirect |
| 46. #14583810 | C2×C4 | semidirect |
| 59. C2×Q8×C173 | C2×C4 | semidirect |
| 61. C2×D4×C173 | C2×C4 | semidirect |
| 129. C173 | #1906 | semidirect |
| 135. #410 | D173 | semidirect |
| 168. C2×Q8 | C4×D173 | semidirect |
| 172. C2×D4 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012289 | 2 |
| #26011959 | 2 |
| #26011509 | 2 |
| C2×#19149606 | 2 |
| #26011261 | 2 |
| #26011250 | 2 |
| #410×C173 | 2 |
| #1906 | 173 |