Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
788 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 788 conjugacy classes of subgroups — too many to draw. Only its 202 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×#19149758 | C2 | semidirect |
| 2. #26012472 | C2 | direct (N × H) |
| 3. C2×#19149738 | C2 | semidirect |
| 6. #19149758 | C22 | semidirect |
| 10. #19149738 | C22 | semidirect |
| 14. C2×#14583827 | C4 | semidirect |
| 16. C22×D692 | C4 | semidirect |
| 18. C22×C4×D173 | C4 | semidirect |
| 20. C22×Q8×C173 | C4 | semidirect |
| 37. C2×D692 | C2×C4 | semidirect |
| 44. C2×C4×D173 | C2×C4 | semidirect |
| 51. C2×Q8×C173 | C2×C4 | semidirect |
| 107. C2×C173 | #410 | semidirect |
| 112. C173 | C2×#410 | semidirect |
| 123. C22×Q8 | #10621924 | semidirect |
| 142. C2×Q8 | C2×#10621924 | semidirect |
| 223. C2 | #26012472 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149758 | 2 |
| #26012472 | 2 |
| C2×#19149738 | 2 |
| C22×#14583827 | 2 |
| C2×#410 | 173 |