Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
402 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012069 | C2 | semidirect |
| 2. #26011822 | C2 | semidirect |
| 3. #26011810 | C2 | semidirect |
| 4. #26011749 | C2 | semidirect |
| 5. #26011744 | C2 | semidirect |
| 6. #26011720 | C2 | semidirect |
| 7. #26011655 | C2 | semidirect |
| 8. #26011638 | C2 | semidirect |
| 9. #408×C173 | C2 | semidirect |
| 117. C173 | #3204 | semidirect |
| 127. #408 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012069 | 2 |
| #26011822 | 2 |
| #26011810 | 2 |
| #26011749 | 2 |
| #26011744 | 2 |
| #26011720 | 2 |
| #26011655 | 2 |
| #26011638 | 2 |
| #408×C173 | 2 |
| #3204 | 173 |