Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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. #26011894 | C2 | semidirect |
| 3. #26011865 | C2 | semidirect |
| 4. #26011863 | C2 | semidirect |
| 5. #26011838 | C2 | semidirect |
| 6. C8×#13063436 | C2 | semidirect |
| 7. #486×C173 | C2 | semidirect |
| 46. #13063436 | D8 | semidirect |
| 47. #13063436 | SD16 | semidirect |
| 75. C173 | #1706 | semidirect |
| 82. #486 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011894 | 2 |
| #26011867 | 2 |
| #26011865 | 2 |
| #26011863 | 2 |
| #26011838 | 2 |
| C8×#13063436 | 2 |
| #486×C173 | 2 |
| #1706 | 173 |