Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 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. #26011857 | C2 | semidirect |
| 3. #26011839 | C2 | semidirect |
| 4. #26011788 | C2 | semidirect |
| 5. #26011768 | C2 | semidirect |
| 6. #26011691 | C2 | semidirect |
| 7. #26011691 | C2 | semidirect |
| 8. #26011622 | C2 | semidirect |
| 9. #26011589 | C2 | semidirect |
| 10. C4×#14583813 | C2 | semidirect |
| 11. #557×C173 | C2 | semidirect |
| 93. Q8×C173 | #41 | semidirect |
| 124. C173 | #3368 | semidirect |
| 126. #557 | D173 | semidirect |
| 204. Q8 | #14583827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012163 | 2 |
| #26011857 | 2 |
| #26011839 | 2 |
| #26011788 | 2 |
| #26011768 | 2 |
| #26011691 | 2 |
| #26011622 | 2 |
| #26011589 | 2 |
| C4×#14583813 | 2 |
| #557×C173 | 2 |
| #3368 | 173 |