Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
924 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 277 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×D692 | C2 | semidirect |
| 3. #26011393 | C2 | semidirect |
| 4. #26011361 | C2 | semidirect |
| 5. C43×C173 | C2 | semidirect |
| 8. #19149676 | C4 | direct (N × H) |
| 18. C2×D692 | C2×C4 | semidirect |
| 27. C42×C173 | C2×C4 | semidirect |
| 28. C42×C173 | D4 | semidirect |
| 49. C4×C173 | C4×D4 | semidirect |
| 50. C4×C173 | #127 | semidirect |
| 56. C173 | C4×#127 | semidirect |
| 62. C43 | D173 | semidirect |
| 84. C42 | C4×D173 | semidirect |
| 85. C42 | D692 | semidirect |
| 107. C4 | C4×D692 | semidirect |
| 108. C4 | #19149676 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149676 | 2 |
| C2×C4×D692 | 2 |
| #26011393 | 2 |
| #26011361 | 2 |
| C43×C173 | 2 |
| C4×#127 | 173 |