Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
402 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 402 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. #26012046 | C2 | semidirect |
| 3. #26011864 | C2 | semidirect |
| 4. #26011843 | C2 | semidirect |
| 5. #26011839 | C2 | semidirect |
| 6. #26011738 | C2 | semidirect |
| 7. #26011590 | C2 | semidirect |
| 8. C4×#14583809 | C2 | semidirect |
| 9. #500×C173 | C2 | semidirect |
| 90. C8×C173 | #41 | semidirect |
| 112. C173 | #3182 | semidirect |
| 116. #500 | D173 | semidirect |
| 203. C8 | #14583827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012046 | 2 |
| #26012042 | 2 |
| #26011864 | 2 |
| #26011843 | 2 |
| #26011839 | 2 |
| #26011738 | 2 |
| #26011590 | 2 |
| C4×#14583809 | 2 |
| #500×C173 | 2 |
| #3182 | 173 |