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. #26012041 | C2 | semidirect |
| 2. C4×#14583826 | C2 | semidirect |
| 3. #26011816 | C2 | semidirect |
| 4. #26011777 | C2 | semidirect |
| 5. #26011772 | C2 | semidirect |
| 6. #26011692 | C2 | semidirect |
| 7. #26011687 | C2 | semidirect |
| 8. #26011638 | C2 | semidirect |
| 9. #26011604 | C2 | semidirect |
| 10. #26011593 | C2 | semidirect |
| 11. #432×C173 | C2 | semidirect |
| 87. Dic346 | #41 | semidirect |
| 93. D692 | #41 | semidirect |
| 144. C173 | #3115 | semidirect |
| 156. #432 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| C4×#14583826 | 2 |
| #26011816 | 2 |
| #26011777 | 2 |
| #26011772 | 2 |
| #26011692 | 2 |
| #26011687 | 2 |
| #26011638 | 2 |
| #26011604 | 2 |
| #26011593 | 2 |
| #432×C173 | 2 |
| #3115 | 173 |