Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
1232 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 349 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. C22×#14583805 | C2 | semidirect |
| 4. #26011350 | C2 | direct (N × H) |
| 5. C2×#19149586 | C2 | semidirect |
| 6. C2×#95×C173 | C2 | semidirect |
| 11. C22×C4×D173 | C4 | semidirect |
| 14. C2×#14583805 | C22 | semidirect |
| 17. #19149586 | C22 | semidirect |
| 20. #95×C173 | C22 | semidirect |
| 36. C2×C4×D173 | C2×C4 | semidirect |
| 53. C22×D173 | C4⋊C4 | semidirect |
| 61. C2×Dic173 | C22⋊C4 | semidirect |
| 93. C2×D173 | C2×C4⋊C4 | semidirect |
| 97. Dic173 | C2×C22⋊C4 | semidirect |
| 98. C2×C173 | #380 | semidirect |
| 105. C173 | C2×#380 | semidirect |
| 112. C2×#95 | D173 | semidirect |
| 126. #95 | C2×D173 | semidirect |
| 205. C2 | #26011350 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D173 | 2 |
| C22×#14583805 | 2 |
| C22×#14583803 | 2 |
| #26011350 | 2 |
| C2×#19149586 | 2 |
| C2×#95×C173 | 2 |
| C2×#380 | 173 |