Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 484 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. #26011856 | C2 | semidirect |
| 4. #26011838 | C2 | semidirect |
| 5. #26011497 | C2 | semidirect |
| 6. C4×M16×C173 | C2 | semidirect |
| 9. #19149679 | C22 | semidirect |
| 13. #19149671 | C22 | semidirect |
| 17. #19149601 | C22 | semidirect |
| 20. #97×C173 | C22 | semidirect |
| 21. C4×C8×C173 | C22 | semidirect |
| 74. C173 | #3138 | semidirect |
| 81. C4×M16 | D173 | semidirect |
| 95. #97 | C2×D173 | semidirect |
| 96. C4×C8 | C2×D173 | 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 |
| #26011856 | 2 |
| #26011838 | 2 |
| #26011497 | 2 |
| C4×M16×C173 | 2 |
| #3138 | 173 |