Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
216 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 77 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. #26011540 | C2 | semidirect |
| 4. M16×Dic173 | C2 | semidirect |
| 5. #26011263 | C2 | semidirect |
| 6. #26011252 | C2 | semidirect |
| 21. #101×C173 | C4 | semidirect |
| 22. #100×C173 | C4 | semidirect |
| 95. C173 | #1932 | semidirect |
| 115. #101 | Dic173 | semidirect |
| 116. #100 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011540 | 2 |
| #26011508 | 2 |
| C2×#19149606 | 2 |
| M16×Dic173 | 2 |
| #26011263 | 2 |
| #26011252 | 2 |
| #413×C173 | 2 |
| #1932 | 173 |