Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19149727 | C2 | semidirect |
| 2. C2×#19149707 | C2 | semidirect |
| 3. C22×#14583813 | C2 | semidirect |
| 4. #26012060 | C2 | semidirect |
| 5. #26011639 | C2 | semidirect |
| 6. #26011631 | C2 | semidirect |
| 7. #26011485 | C2 | semidirect |
| 8. #26011459 | C2 | semidirect |
| 9. #419×C173 | C2 | semidirect |
| 13. C2×#14583827 | C22 | semidirect |
| 18. C2×Q8×D173 | C22 | semidirect |
| 30. #19149602 | C22 | semidirect |
| 31. #19149599 | C22 | semidirect |
| 32. #19149591 | C22 | semidirect |
| 36. #103×C173 | C22 | semidirect |
| 45. #14583826 | D4 | semidirect |
| 74. C2×Q8×C173 | D4 | semidirect |
| 145. C173 | #3010 | semidirect |
| 153. #419 | D173 | semidirect |
| 180. #103 | C2×D173 | semidirect |
| 200. C2×Q8 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149727 | 2 |
| C2×#19149707 | 2 |
| C22×#14583813 | 2 |
| #26012060 | 2 |
| #26011639 | 2 |
| #26011631 | 2 |
| #26011485 | 2 |
| #26011459 | 2 |
| #419×C173 | 2 |
| #3010 | 173 |