Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
856 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 218 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 |
|---|---|---|
| 1. C22×#14583836 | C2 | semidirect |
| 2. C22×C4×#10621924 | C2 | semidirect |
| 3. C2×#19149744 | C2 | direct (N × H) |
| 7. C2×#14583836 | C22 | semidirect |
| 10. C2×C4×#10621924 | C22 | semidirect |
| 11. #19149744 | C22 | direct (N × H) |
| 14. C2×#14583827 | C4 | semidirect |
| 17. C22×D692 | C4 | semidirect |
| 20. C22×Q8×C173 | C4 | semidirect |
| 24. #14583836 | C23 | semidirect |
| 27. C4×#10621924 | C23 | semidirect |
| 33. #14583827 | C2×C4 | semidirect |
| 38. C2×D692 | C2×C4 | semidirect |
| 47. C2×Q8×C173 | C2×C4 | semidirect |
| 61. D692 | C22×C4 | semidirect |
| 73. Q8×C173 | C22×C4 | semidirect |
| 77. C22×C173 | #104 | semidirect |
| 91. C2×C173 | C2×#104 | semidirect |
| 96. C173 | C22×#104 | semidirect |
| 106. C22×Q8 | #10621924 | semidirect |
| 126. C2×Q8 | C2×#10621924 | semidirect |
| 154. Q8 | C22×#10621924 | semidirect |
| 180. C22 | #19149744 | direct (N × H) |
| 191. C2 | C2×#19149744 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583836 | 2 |
| C22×C4×#10621924 | 2 |
| C2×#19149744 | 2 |
| C22×#14583827 | 2 |
| C22×#104 | 173 |