Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. Q8×Dic346 | C2 | semidirect |
| 3. #26011838 | C2 | semidirect |
| 4. #26011836 | C2 | semidirect |
| 5. #26011781 | C2 | semidirect |
| 6. #26011780 | C2 | semidirect |
| 7. #26011691 | C2 | semidirect |
| 8. #26011689 | C2 | semidirect |
| 9. C8×Dic346 | C2 | semidirect |
| 10. #26011576 | C2 | semidirect |
| 11. C4×SD16×C173 | C2 | semidirect |
| 77. Dic346 | SD16 | semidirect |
| 91. Q8×C173 | #41 | semidirect |
| 125. C173 | #3362 | semidirect |
| 137. C4×SD16 | D173 | semidirect |
| 206. Q8 | #14583826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic346 | 2 |
| #26012162 | 2 |
| #26011838 | 2 |
| #26011836 | 2 |
| #26011781 | 2 |
| #26011780 | 2 |
| #26011691 | 2 |
| #26011689 | 2 |
| C8×Dic346 | 2 |
| #26011576 | 2 |
| C4×SD16×C173 | 2 |
| #3362 | 173 |