Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 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 |
|---|---|---|
| 2. #26011692 | C2 | semidirect |
| 3. C8×Dic346 | C2 | semidirect |
| 4. #26011234 | C2 | semidirect |
| 5. #335×C173 | C2 | semidirect |
| 34. Dic346 | D8 | semidirect |
| 48. C8×C173 | SD16 | semidirect |
| 64. C173 | #1668 | semidirect |
| 69. #335 | D173 | semidirect |
| 113. C8 | #14583815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011868 | 2 |
| #26011692 | 2 |
| C8×Dic346 | 2 |
| #26011234 | 2 |
| #335×C173 | 2 |
| #1668 | 173 |