Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26011865 | C2 | semidirect |
| 3. #26011839 | C2 | semidirect |
| 4. C8×#13063436 | C2 | semidirect |
| 5. #500×C173 | C2 | semidirect |
| 32. #13063436 | D8 | semidirect |
| 38. C8×C173 | SD16 | semidirect |
| 51. C173 | #1706 | semidirect |
| 53. #500 | D173 | semidirect |
| 90. C8 | #14583813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011868 | 2 |
| #26011865 | 2 |
| #26011839 | 2 |
| C8×#13063436 | 2 |
| #500×C173 | 2 |
| #1706 | 173 |