Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
848 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 104 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. C2×#19149741 | C2 | semidirect |
| 2. D173⋊(C22⋊C8) | C2 | semidirect |
| 3. #26012433 | C2 | semidirect |
| 5. C2×D173⋊C8 | C22 | semidirect |
| 6. C2×C4⋊#10621924 | C22 | semidirect |
| 13. C22×D692 | C4 | semidirect |
| 18. C2×D4×D173 | C4 | semidirect |
| 21. C22×D4×C173 | C4 | semidirect |
| 83. D692 | C22⋊C4 | semidirect |
| 100. D4×C173 | C22⋊C4 | semidirect |
| 110. C22×C173 | #102 | semidirect |
| 123. C2×D173 | #102 | semidirect |
| 142. C173 | #1786 | semidirect |
| 156. C22×D4 | #10621924 | semidirect |
| 232. D4 | C22⋊#10621924 | semidirect |
| 269. C22 | #19149741 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149741 | 2 |
| D173⋊(C22⋊C8) | 2 |
| #26012433 | 2 |
| C22×D4×D173 | 2 |
| #1786 | 173 |