Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
544 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 205 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×C4×Dic346 | C2 | semidirect |
| 4. #26011593 | C2 | direct (N × H) |
| 5. C2×#19149613 | C2 | semidirect |
| 6. C2×#19149604 | C2 | semidirect |
| 8. C2×#97×C173 | C2 | semidirect |
| 12. C2×#14583815 | C4 | semidirect |
| 15. C4×Dic346 | C22 | semidirect |
| 23. #19149613 | C22 | semidirect |
| 24. #19149604 | C22 | semidirect |
| 29. #97×C173 | C22 | semidirect |
| 33. C2×Dic346 | C2×C4 | semidirect |
| 44. #14583815 | C2×C4 | semidirect |
| 56. C2×C8×C173 | C2×C4 | semidirect |
| 67. Dic346 | C22×C4 | semidirect |
| 88. C8×C173 | C22×C4 | semidirect |
| 105. C2×C173 | #440 | semidirect |
| 110. C173 | C2×#440 | semidirect |
| 119. C2×#97 | D173 | semidirect |
| 140. #97 | C2×D173 | semidirect |
| 160. C2×C8 | C4×D173 | semidirect |
| 199. C8 | C2×C4×D173 | semidirect |
| 217. C2 | #26011593 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583815 | 2 |
| C2×C4×Dic346 | 2 |
| C2×C4×D692 | 2 |
| #26011593 | 2 |
| C2×#19149613 | 2 |
| C2×#19149604 | 2 |
| C2×#19149601 | 2 |
| C2×#97×C173 | 2 |
| C2×#440 | 173 |