Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26012048 | C2 | semidirect |
| 3. #26011864 | C2 | semidirect |
| 4. #26011838 | C2 | semidirect |
| 5. #26011692 | C2 | semidirect |
| 6. #26011644 | C2 | semidirect |
| 7. #431×C173 | C2 | semidirect |
| 11. C2×#14583815 | C22 | semidirect |
| 12. #19149679 | C22 | semidirect |
| 13. #19149679 | C22 | semidirect |
| 22. C4×Dic346 | C22 | semidirect |
| 24. #19149601 | C22 | semidirect |
| 26. C4⋊C8×C173 | C22 | semidirect |
| 28. C4×C8×C173 | C22 | semidirect |
| 75. C2×C4×C173 | SD16 | semidirect |
| 104. C173 | #3208 | semidirect |
| 112. #431 | D173 | semidirect |
| 130. C4⋊C8 | C2×D173 | semidirect |
| 133. C4×C8 | C2×D173 | semidirect |
| 180. C2×C4 | #14583815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012048 | 2 |
| C2×#19149676 | 2 |
| #26011864 | 2 |
| #26011838 | 2 |
| #26011692 | 2 |
| #26011644 | 2 |
| #431×C173 | 2 |
| #3208 | 173 |