Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1104 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 269 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. C2×#19149638 | C2 | semidirect |
| 3. #26011393 | C2 | semidirect |
| 4. #26011392 | C2 | semidirect |
| 5. #26011346 | C2 | semidirect |
| 6. C2×#117×C173 | C2 | semidirect |
| 10. C22×D692 | C4 | semidirect |
| 14. C2×C4⋊Dic173 | C22 | semidirect |
| 16. C2×#14583803 | C22 | semidirect |
| 17. C2×C4×Dic173 | C22 | semidirect |
| 20. C2×C4⋊C4×C173 | C22 | semidirect |
| 22. C2×C42×C173 | C22 | semidirect |
| 69. C2×C4×C173 | C22⋊C4 | semidirect |
| 99. C173 | #2309 | semidirect |
| 103. C2×#117 | D173 | semidirect |
| 117. C2×C4⋊C4 | C2×D173 | semidirect |
| 122. C2×C42 | C2×D173 | semidirect |
| 169. C2×C4 | #14583803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D692 | 2 |
| C2×#19149638 | 2 |
| #26011393 | 2 |
| #26011392 | 2 |
| #26011346 | 2 |
| C2×#117×C173 | 2 |
| #2309 | 173 |