Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26011795 | C2 | semidirect |
| 3. #26011788 | C2 | semidirect |
| 4. #26011783 | C2 | semidirect |
| 5. #26011768 | C2 | semidirect |
| 6. #26011534 | C2 | semidirect |
| 7. C2×#19149612 | C2 | semidirect |
| 8. #26011518 | C2 | semidirect |
| 11. #544×C173 | C2 | semidirect |
| 42. #14583826 | Q8 | semidirect |
| 123. C173 | #3083 | semidirect |
| 125. #544 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011971 | 2 |
| #26011795 | 2 |
| #26011788 | 2 |
| #26011783 | 2 |
| #26011768 | 2 |
| #26011534 | 2 |
| C2×#19149612 | 2 |
| #26011518 | 2 |
| #26011490 | 2 |
| #26011485 | 2 |
| #544×C173 | 2 |
| #3083 | 173 |