Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26011889 | C2 | semidirect |
| 3. #26011776 | C2 | semidirect |
| 5. #26011236 | C2 | semidirect |
| 7. Q8⋊C8×C173 | C2 | semidirect |
| 66. Q8×C173 | SD16 | semidirect |
| 92. C173 | #1651 | semidirect |
| 99. Q8⋊C8 | D173 | semidirect |
| 150. Q8 | #14583815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D692 | 2 |
| #26011889 | 2 |
| #26011776 | 2 |
| #26011697 | 2 |
| #26011236 | 2 |
| #26011220 | 2 |
| Q8⋊C8×C173 | 2 |
| #1651 | 173 |