Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. Q8×#13063436 | C2 | semidirect |
| 4. #26011241 | C2 | semidirect |
| 5. #26011237 | C2 | semidirect |
| 7. #475×C173 | C2 | semidirect |
| 51. #13063436 | SD16 | semidirect |
| 55. Q8×C173 | SD16 | semidirect |
| 79. C173 | #1666 | semidirect |
| 82. #475 | D173 | semidirect |
| 126. Q8 | #14583813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011865 | 2 |
| #26011691 | 2 |
| Q8×#13063436 | 2 |
| #26011241 | 2 |
| #26011237 | 2 |
| #26011234 | 2 |
| #475×C173 | 2 |
| #1666 | 173 |