Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
532 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 532 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. #26012041 | C2 | semidirect |
| 2. C2×#19149676 | C2 | semidirect |
| 3. #26011868 | C2 | semidirect |
| 4. #26011838 | C2 | semidirect |
| 5. #26011687 | C2 | semidirect |
| 6. #26011627 | C2 | semidirect |
| 7. #431×C173 | C2 | semidirect |
| 12. C2×D1384 | C22 | semidirect |
| 13. #19149679 | C22 | semidirect |
| 18. #19149676 | C22 | semidirect |
| 23. C4×D692 | C22 | semidirect |
| 24. #19149601 | C22 | semidirect |
| 26. C4⋊C8×C173 | C22 | semidirect |
| 28. C4×C8×C173 | C22 | semidirect |
| 80. C2×C4×C173 | D8 | semidirect |
| 112. C173 | #3205 | semidirect |
| 120. #431 | D173 | semidirect |
| 138. C4⋊C8 | C2×D173 | semidirect |
| 141. C4×C8 | C2×D173 | semidirect |
| 193. C2×C4 | D1384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| C2×#19149676 | 2 |
| #26011868 | 2 |
| #26011838 | 2 |
| #26011687 | 2 |
| #26011627 | 2 |
| #431×C173 | 2 |
| #3205 | 173 |