Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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. #26011899 | C2 | semidirect |
| 4. #26011898 | C2 | semidirect |
| 5. #26011893 | C2 | semidirect |
| 6. #26011890 | C2 | semidirect |
| 7. #26011890 | C2 | semidirect |
| 11. #499×C173 | C2 | semidirect |
| 43. #14583809 | Q8 | semidirect |
| 44. #14583809 | Q8 | semidirect |
| 99. C173 | #3166 | semidirect |
| 108. #499 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012047 | 2 |
| #125×D173 | 2 |
| #26011899 | 2 |
| #26011898 | 2 |
| #26011893 | 2 |
| #26011890 | 2 |
| #26011532 | 2 |
| #26011530 | 2 |
| C4×#14583809 | 2 |
| #499×C173 | 2 |
| #3166 | 173 |