Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
316 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#19149614 | C2 | semidirect |
| 3. #26011495 | C2 | semidirect |
| 4. C2×#19149596 | C2 | semidirect |
| 5. C2×#19149595 | C2 | semidirect |
| 6. #26011447 | C2 | semidirect |
| 7. #418×C173 | C2 | semidirect |
| 12. C2×#14583811 | C4 | semidirect |
| 111. C173 | #1978 | semidirect |
| 116. #418 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583811 | 2 |
| C2×#19149614 | 2 |
| #26011495 | 2 |
| C2×#19149596 | 2 |
| C2×#19149595 | 2 |
| #26011447 | 2 |
| #418×C173 | 2 |
| #1978 | 173 |