Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
412 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26012046 | C2 | semidirect |
| 3. #26011889 | C2 | semidirect |
| 4. #26011841 | C2 | semidirect |
| 5. #26011837 | C2 | semidirect |
| 6. #26011717 | C2 | semidirect |
| 7. SD16×Dic173 | C2 | semidirect |
| 8. C4×C8×D173 | C2 | semidirect |
| 9. #492×C173 | C2 | semidirect |
| 79. C4×D173 | SD16 | semidirect |
| 90. C8×C173 | #41 | semidirect |
| 112. C173 | #3167 | semidirect |
| 117. #492 | D173 | semidirect |
| 203. C8 | #14583825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012046 | 2 |
| #26012039 | 2 |
| #26011889 | 2 |
| #26011841 | 2 |
| #26011837 | 2 |
| #26011717 | 2 |
| SD16×Dic173 | 2 |
| C4×C8×D173 | 2 |
| #492×C173 | 2 |
| #3167 | 173 |