Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #26011599 | C2 | semidirect |
| 4. #26011598 | C2 | semidirect |
| 5. #26011597 | C2 | semidirect |
| 6. C4×#14583816 | C2 | semidirect |
| 7. #26011583 | C2 | semidirect |
| 11. #441×C173 | C2 | semidirect |
| 15. Q16×D173 | C4 | semidirect |
| 108. C173 | #2950 | semidirect |
| 115. #441 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D173 | 2 |
| #26011967 | 2 |
| #26011599 | 2 |
| #26011598 | 2 |
| #26011597 | 2 |
| C4×#14583816 | 2 |
| #26011583 | 2 |
| #26011526 | 2 |
| #26011498 | 2 |
| #26011448 | 2 |
| #441×C173 | 2 |
| #2950 | 173 |