Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
186 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 51 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×#19149620 | C2 | semidirect |
| 2. #26011866 | C2 | semidirect |
| 3. D8×Dic173 | C2 | semidirect |
| 4. #26011309 | C2 | semidirect |
| 5. #26011293 | C2 | semidirect |
| 6. #26011292 | C2 | semidirect |
| 7. C2×D16×C173 | C2 | semidirect |
| 38. D8×C173 | D4 | semidirect |
| 74. Dic173 | D16 | semidirect |
| 81. C173 | #2206 | semidirect |
| 84. C2×D16 | D173 | semidirect |
| 115. D8 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149620 | 2 |
| #26011866 | 2 |
| D8×Dic173 | 2 |
| #26011309 | 2 |
| #26011293 | 2 |
| #26011292 | 2 |
| C2×D16×C173 | 2 |
| #2206 | 173 |