Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 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. #26012211 | C2 | semidirect |
| 2. #26011837 | C2 | semidirect |
| 3. #26011812 | C2 | semidirect |
| 4. #26011776 | C2 | semidirect |
| 5. #26011718 | C2 | semidirect |
| 6. #26011688 | C2 | semidirect |
| 7. #26011653 | C2 | semidirect |
| 8. C4×#14583816 | C2 | semidirect |
| 9. D4×#13063436 | C2 | semidirect |
| 10. #26011487 | C2 | semidirect |
| 127. C173 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012211 | 2 |
| #26011837 | 2 |
| #26011812 | 2 |
| #26011776 | 2 |
| #26011718 | 2 |
| #26011688 | 2 |
| #26011653 | 2 |
| C4×#14583816 | 2 |
| D4×#13063436 | 2 |
| #26011487 | 2 |
| #550×C173 | 2 |
| #3304 | 173 |