Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
488 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 213 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. #26011547 | C2 | direct (N × H) |
| 3. C2×C4⋊#13063436 | C2 | semidirect |
| 5. C2×#19149589 | C2 | semidirect |
| 6. C2×C4⋊C8×C173 | C2 | semidirect |
| 16. C4⋊#13063436 | C22 | semidirect |
| 18. #19149589 | C22 | semidirect |
| 21. C4⋊C8×C173 | C22 | semidirect |
| 89. C2×C173 | #432 | semidirect |
| 94. C173 | C2×#432 | semidirect |
| 99. C2×C4⋊C8 | D173 | semidirect |
| 114. C4⋊C8 | C2×D173 | semidirect |
| 185. C2 | #26011547 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D173 | 2 |
| #26011547 | 2 |
| C2×C4⋊#13063436 | 2 |
| C2×#19149591 | 2 |
| C2×#19149589 | 2 |
| C2×C4⋊C8×C173 | 2 |
| C2×#432 | 173 |