Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
388 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26011841 | C2 | semidirect |
| 3. #26011824 | C2 | semidirect |
| 4. #26011786 | C2 | semidirect |
| 5. #26011730 | C2 | semidirect |
| 6. #26011698 | C2 | semidirect |
| 7. #26011647 | C2 | semidirect |
| 8. C4×#14583816 | C2 | semidirect |
| 10. C2×#19149603 | C2 | semidirect |
| 92. D4×C173 | Q16 | semidirect |
| 122. C173 | #3299 | semidirect |
| 208. D4 | #14583816 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012198 | 2 |
| #26011841 | 2 |
| #26011824 | 2 |
| #26011786 | 2 |
| #26011730 | 2 |
| #26011698 | 2 |
| #26011647 | 2 |
| C4×#14583816 | 2 |
| D4×#13063436 | 2 |
| C2×#19149603 | 2 |
| D4×Q8×C173 | 2 |
| #3299 | 173 |