Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
436 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 3. C2×C8×#10621924 | C2 | semidirect |
| 4. (C2×#10621924)⋊C8 | C2 | semidirect |
| 12. #19149736 | C4 | semidirect |
| 13. C22⋊#13063443 | C4 | semidirect |
| 17. C22⋊#13063436 | C4 | semidirect |
| 18. #19149591 | C4 | semidirect |
| 19. C22⋊C8×C173 | C4 | semidirect |
| 22. C22×#10621924 | C8 | semidirect |
| 27. C2×#13063443 | C2×C4 | semidirect |
| 39. C2×#13063436 | C2×C4 | semidirect |
| 43. C2×C8×C173 | C2×C4 | semidirect |
| 75. C22×C173 | C4×C8 | semidirect |
| 81. C2×D173 | C4×C8 | semidirect |
| 87. #10621924 | C22⋊C8 | direct (N × H) |
| 99. C173 | C4×C22⋊C8 | semidirect |
| 118. C22⋊C8 | #10621924 | direct (N × H) |
| 140. C2×C8 | C2×#10621924 | semidirect |
| 184. C22 | C8×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#10621924 | 2 |
| D173⋊(C22⋊C8) | 2 |
| C2×C8×#10621924 | 2 |
| (C2×#10621924)⋊C8 | 2 |
| C22⋊C8×D173 | 2 |
| C4×C22⋊C8 | 173 |