Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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. #26011895 | C2 | semidirect |
| 3. #26011869 | C2 | semidirect |
| 4. #26011840 | C2 | semidirect |
| 7. Q16×Dic173 | C2 | semidirect |
| 8. #26011585 | C2 | semidirect |
| 9. #26011583 | C2 | semidirect |
| 77. C2×Dic173 | Q16 | semidirect |
| 114. C173 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012043 | 2 |
| #26011895 | 2 |
| #26011869 | 2 |
| #26011840 | 2 |
| #26011732 | 2 |
| #26011730 | 2 |
| Q16×Dic173 | 2 |
| #26011585 | 2 |
| #26011583 | 2 |
| C2×C8×Dic173 | 2 |
| #467×C173 | 2 |
| #3170 | 173 |