Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26012039 | C2 | semidirect |
| 2. C4×#14583825 | C2 | semidirect |
| 3. #26011814 | C2 | semidirect |
| 4. #26011777 | C2 | semidirect |
| 5. #26011771 | C2 | semidirect |
| 6. #26011688 | C2 | semidirect |
| 7. #26011633 | C2 | semidirect |
| 8. #26011603 | C2 | semidirect |
| 9. #26011588 | C2 | semidirect |
| 10. #26011547 | C2 | semidirect |
| 11. #459×C173 | C2 | semidirect |
| 86. Dic346 | #41 | semidirect |
| 110. D4×C173 | #41 | semidirect |
| 144. C173 | #3115 | semidirect |
| 152. #459 | D173 | semidirect |
| 241. D4 | #14583825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012039 | 2 |
| C4×#14583825 | 2 |
| #26011814 | 2 |
| #26011777 | 2 |
| #26011771 | 2 |
| #26011688 | 2 |
| #26011633 | 2 |
| #26011603 | 2 |
| #26011588 | 2 |
| #26011547 | 2 |
| #459×C173 | 2 |
| #3115 | 173 |