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 |
|---|---|---|
| 2. #26011857 | C2 | semidirect |
| 3. #26011839 | C2 | semidirect |
| 4. #26011495 | C2 | semidirect |
| 5. C4×#14583810 | C2 | semidirect |
| 6. #533×C173 | C2 | semidirect |
| 13. #19149599 | C22 | semidirect |
| 14. #19149590 | C22 | semidirect |
| 15. C4×#13063436 | C22 | semidirect |
| 16. C4⋊Q8×C173 | C22 | semidirect |
| 17. #125×C173 | C22 | semidirect |
| 74. C173 | #3138 | semidirect |
| 76. #533 | D173 | semidirect |
| 85. C4⋊Q8 | C2×D173 | semidirect |
| 89. #125 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149676 | 2 |
| #26011857 | 2 |
| #26011839 | 2 |
| #26011495 | 2 |
| C4×#14583810 | 2 |
| #533×C173 | 2 |
| #3138 | 173 |