Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26011972 | C2 | semidirect |
| 3. C2×#19149607 | C2 | semidirect |
| 4. #26011496 | C2 | semidirect |
| 5. #26011260 | C2 | semidirect |
| 6. #26011251 | C2 | semidirect |
| 7. #390×C173 | C2 | semidirect |
| 10. #19149705 | C4 | semidirect |
| 42. #14583810 | C2×C4 | semidirect |
| 58. C2×D4×C173 | C2×C4 | semidirect |
| 69. Dic346 | C22⋊C4 | semidirect |
| 71. D692 | C22⋊C4 | semidirect |
| 132. C173 | #1883 | semidirect |
| 138. #390 | D173 | semidirect |
| 174. C2×D4 | C4×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149705 | 2 |
| #26011972 | 2 |
| C2×#19149607 | 2 |
| #26011496 | 2 |
| #26011260 | 2 |
| #26011251 | 2 |
| #390×C173 | 2 |
| #1883 | 173 |