Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
248 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 78 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. #26012341 | C2 | semidirect |
| 4. Q8⋊#13063443 | C2 | semidirect |
| 28. Q8×D173 | C8 | semidirect |
| 93. C173 | #1479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012510 | 2 |
| #26012509 | 2 |
| #26012341 | 2 |
| Q8⋊#13063443 | 2 |
| C4×Q8×D173 | 2 |
| #1479 | 173 |