Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
262 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. #26011540 | C2 | semidirect |
| 3. #26011515 | C2 | semidirect |
| 5. #26011263 | C2 | semidirect |
| 6. #26011251 | C2 | semidirect |
| 21. #104×C173 | C4 | semidirect |
| 22. #104×C173 | C4 | semidirect |
| 97. C173 | #1861 | semidirect |
| 119. #104 | Dic173 | semidirect |
| 120. #104 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012258 | 2 |
| #26011540 | 2 |
| #26011515 | 2 |
| #26011508 | 2 |
| #26011263 | 2 |
| #26011251 | 2 |
| C2×#104×C173 | 2 |
| #1861 | 173 |