Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 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. #26011842 | C2 | semidirect |
| 4. #26011828 | C2 | semidirect |
| 5. #26011786 | C2 | semidirect |
| 6. #26011731 | C2 | semidirect |
| 7. #26011701 | C2 | semidirect |
| 8. #26011645 | C2 | semidirect |
| 10. #103×D173 | C2 | semidirect |
| 11. C4×Q16×C173 | C2 | semidirect |
| 81. D692 | Q16 | semidirect |
| 122. C173 | #3299 | semidirect |
| 132. C4×Q16 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012201 | 2 |
| Q8×D692 | 2 |
| #26011842 | 2 |
| #26011828 | 2 |
| #26011786 | 2 |
| #26011731 | 2 |
| #26011701 | 2 |
| #26011645 | 2 |
| C8×D692 | 2 |
| #103×D173 | 2 |
| C4×Q16×C173 | 2 |
| #3299 | 173 |