Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #26011848 | C2 | semidirect |
| 4. #26011788 | C2 | semidirect |
| 5. #26011773 | C2 | semidirect |
| 6. #26011713 | C2 | semidirect |
| 8. Q8×#13063436 | C2 | semidirect |
| 9. C4×#14583816 | C2 | semidirect |
| 10. C4×#14583813 | C2 | semidirect |
| 11. #557×C173 | C2 | semidirect |
| 117. C173 | #3365 | semidirect |
| 120. #557 | 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 |
| #26011773 | 2 |
| #26011713 | 2 |
| #26011691 | 2 |
| Q8×#13063436 | 2 |
| C4×#14583816 | 2 |
| C4×#14583813 | 2 |
| #557×C173 | 2 |
| #3365 | 173 |