Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
740 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 173 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×#14583816 | C2 | semidirect |
| 4. #26011645 | C2 | direct (N × H) |
| 5. C2×#19149604 | C2 | semidirect |
| 6. C2×#19149603 | C2 | semidirect |
| 8. C22×Q16×C173 | C2 | semidirect |
| 18. C2×#14583816 | C22 | semidirect |
| 25. #19149604 | C22 | semidirect |
| 26. #19149603 | C22 | semidirect |
| 31. C2×Q16×C173 | C22 | semidirect |
| 75. C22×D173 | Q16 | semidirect |
| 115. C2×D173 | C2×Q16 | semidirect |
| 124. C2×C173 | #451 | semidirect |
| 129. C173 | C2×#451 | semidirect |
| 133. C22×Q16 | D173 | semidirect |
| 152. C2×Q16 | C2×D173 | semidirect |
| 255. C2 | #26011645 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D173 | 2 |
| C22×#14583816 | 2 |
| C2×#19149655 | 2 |
| #26011645 | 2 |
| C2×#19149604 | 2 |
| C2×#19149603 | 2 |
| C2×#19149591 | 2 |
| C22×Q16×C173 | 2 |
| C2×#451 | 173 |