Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
652 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 209 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. C2×#19149644 | C2 | semidirect |
| 4. #26011396 | C2 | semidirect |
| 6. #26011380 | C2 | semidirect |
| 7. #26011338 | C2 | semidirect |
| 8. C42×Dic173 | C2 | semidirect |
| 9. #382×C173 | C2 | semidirect |
| 13. #19149667 | C4 | semidirect |
| 33. C2×Dic346 | C2×C4 | semidirect |
| 46. #14583803 | C2×C4 | semidirect |
| 58. C42×C173 | C2×C4 | semidirect |
| 105. Dic173 | #124 | semidirect |
| 112. C173 | C4×#124 | semidirect |
| 120. #382 | D173 | semidirect |
| 171. C42 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149667 | 2 |
| C2×#19149644 | 2 |
| C2×#19149641 | 2 |
| #26011396 | 2 |
| #26011392 | 2 |
| #26011380 | 2 |
| #26011338 | 2 |
| C42×Dic173 | 2 |
| #382×C173 | 2 |
| C4×#124 | 173 |