Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 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 |
|---|---|---|
| 1. C4×#14583826 | C2 | semidirect |
| 2. #26011812 | C2 | semidirect |
| 3. #26011773 | C2 | semidirect |
| 4. #26011768 | C2 | semidirect |
| 5. #26011688 | C2 | semidirect |
| 6. #26011683 | C2 | semidirect |
| 7. #26011634 | C2 | semidirect |
| 8. #26011601 | C2 | semidirect |
| 9. #26011591 | C2 | semidirect |
| 10. #26011548 | C2 | semidirect |
| 11. #532×C173 | C2 | semidirect |
| 85. Dic346 | #41 | semidirect |
| 87. D692 | #41 | semidirect |
| 144. C173 | #3115 | semidirect |
| 146. #532 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14583826 | 2 |
| #26011812 | 2 |
| #26011773 | 2 |
| #26011768 | 2 |
| #26011688 | 2 |
| #26011683 | 2 |
| #26011634 | 2 |
| #26011601 | 2 |
| #26011591 | 2 |
| #26011548 | 2 |
| #532×C173 | 2 |
| #3115 | 173 |