Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
294 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 83 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×#19149670 | C2 | semidirect |
| 5. #26011253 | C2 | semidirect |
| 6. #26011245 | C2 | semidirect |
| 7. #340×C173 | C2 | semidirect |
| 120. C173 | #2025 | semidirect |
| 127. #340 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149670 | 2 |
| C2×#19149601 | 2 |
| C2×#19149599 | 2 |
| #26011392 | 2 |
| #26011253 | 2 |
| #26011245 | 2 |
| #340×C173 | 2 |
| #2025 | 173 |