Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
816 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 816 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. C22×C4⋊Dic173 | C2 | semidirect |
| 3. #26011493 | C2 | direct (N × H) |
| 4. C2×#19149604 | C2 | semidirect |
| 5. C2×#19149601 | C2 | semidirect |
| 6. C22×M16×C173 | C2 | semidirect |
| 9. C2×#14583826 | C4 | semidirect |
| 19. C2×C4⋊Dic173 | C22 | semidirect |
| 20. #19149604 | C22 | semidirect |
| 21. #19149601 | C22 | semidirect |
| 24. C2×M16×C173 | C22 | semidirect |
| 29. #14583826 | C2×C4 | semidirect |
| 32. C2×Dic346 | C2×C4 | semidirect |
| 36. C2×D692 | C2×C4 | semidirect |
| 65. Dic346 | C22×C4 | semidirect |
| 68. D692 | C22×C4 | semidirect |
| 110. C2×C173 | #417 | semidirect |
| 115. C173 | C2×#417 | semidirect |
| 118. C22×M16 | D173 | semidirect |
| 134. C2×M16 | C2×D173 | semidirect |
| 227. C2 | #26011493 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583826 | 2 |
| C22×C4⋊Dic173 | 2 |
| #26011493 | 2 |
| C2×#19149604 | 2 |
| C2×#19149601 | 2 |
| C22×M16×C173 | 2 |
| C2×#417 | 173 |