Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
200 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26011241 | C2 | direct (N × H) |
| 19. C2×#13063436 | C8 | semidirect |
| 33. #13063436 | C2×C8 | semidirect |
| 59. C2×C173 | #334 | semidirect |
| 63. C173 | C2×#334 | semidirect |
| 123. C2 | #26011241 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#13063436 | 2 |
| C2×C4×#13063436 | 2 |
| #26011241 | 2 |
| C2×C4⋊C8×C173 | 2 |
| C2×#334 | 173 |