Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1072 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 258 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×D173⋊C8 | C2 | semidirect |
| 2. C22×C4⋊#10621924 | C2 | semidirect |
| 3. C2×#19149741 | C2 | direct (N × H) |
| 7. C2×D173⋊C8 | C22 | semidirect |
| 10. C2×C4⋊#10621924 | C22 | semidirect |
| 11. #19149741 | C22 | direct (N × H) |
| 13. C22×D692 | C4 | semidirect |
| 17. C2×D4×D173 | C4 | semidirect |
| 20. C22×D4×C173 | C4 | semidirect |
| 24. D173⋊C8 | C23 | semidirect |
| 27. C4⋊#10621924 | C23 | semidirect |
| 35. C2×D692 | C2×C4 | semidirect |
| 41. D4×D173 | C2×C4 | semidirect |
| 50. C2×D4×C173 | C2×C4 | semidirect |
| 67. D692 | C22×C4 | semidirect |
| 81. D4×C173 | C22×C4 | semidirect |
| 86. C22×C173 | #102 | semidirect |
| 93. C2×D173 | #102 | semidirect |
| 104. C2×C173 | C2×#102 | semidirect |
| 107. D173 | C2×#102 | semidirect |
| 110. C173 | C22×#102 | semidirect |
| 123. C22×D4 | #10621924 | semidirect |
| 149. C2×D4 | C2×#10621924 | semidirect |
| 182. D4 | C22×#10621924 | semidirect |
| 207. C22 | #19149741 | direct (N × H) |
| 219. C2 | C2×#19149741 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D173⋊C8 | 2 |
| C22×C4⋊#10621924 | 2 |
| C2×#19149741 | 2 |
| C22×D4×D173 | 2 |
| C22×#102 | 173 |