Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×#14583815 | C2 | semidirect |
| 3. C2×#19149658 | C2 | semidirect |
| 4. #26011644 | C2 | direct (N × H) |
| 5. C2×#19149601 | C2 | semidirect |
| 6. C2×C22⋊C8×C173 | C2 | semidirect |
| 8. C22×Dic346 | C22 | semidirect |
| 15. C2×#14583815 | C22 | semidirect |
| 17. #19149658 | C22 | semidirect |
| 18. C2×C4⋊Dic173 | C22 | semidirect |
| 21. #19149601 | C22 | semidirect |
| 23. C22×C8×C173 | C22 | semidirect |
| 24. C22⋊C8×C173 | C22 | semidirect |
| 32. C2×Dic346 | C23 | semidirect |
| 45. C4⋊Dic173 | C23 | semidirect |
| 55. C2×C8×C173 | C23 | semidirect |
| 76. C23×C173 | SD16 | semidirect |
| 92. C22×C173 | C2×SD16 | semidirect |
| 106. C2×C173 | #450 | semidirect |
| 111. C173 | C2×#450 | semidirect |
| 118. C2×C22⋊C8 | D173 | semidirect |
| 129. C22×C8 | C2×D173 | semidirect |
| 136. C22⋊C8 | C2×D173 | semidirect |
| 163. C2×C8 | C22×D173 | semidirect |
| 178. C23 | #14583815 | semidirect |
| 209. C22 | C2×#14583815 | semidirect |
| 219. C2 | #26011644 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D692 | 2 |
| C22×#14583815 | 2 |
| C2×#19149658 | 2 |
| #26011644 | 2 |
| C2×#19149601 | 2 |
| C2×C22⋊C8×C173 | 2 |
| C2×#450 | 173 |