Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. #26012226 | C2 | semidirect |
| 2. #26011848 | C2 | semidirect |
| 3. #26011839 | C2 | semidirect |
| 4. #26011788 | C2 | semidirect |
| 5. #26011783 | C2 | semidirect |
| 6. #26011706 | C2 | semidirect |
| 8. Q8×#13063436 | C2 | semidirect |
| 9. C4×#14583814 | C2 | semidirect |
| 10. C4×#14583811 | C2 | semidirect |
| 11. #554×C173 | C2 | semidirect |
| 122. C173 | #3361 | semidirect |
| 125. #554 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012226 | 2 |
| #26011848 | 2 |
| #26011839 | 2 |
| #26011788 | 2 |
| #26011783 | 2 |
| #26011706 | 2 |
| #26011686 | 2 |
| Q8×#13063436 | 2 |
| C4×#14583814 | 2 |
| C4×#14583811 | 2 |
| #554×C173 | 2 |
| #3361 | 173 |