Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
438 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×D4×Dic173 | C2 | semidirect |
| 3. C2×#19149601 | C2 | semidirect |
| 4. #26011392 | C2 | semidirect |
| 5. #26011253 | C2 | semidirect |
| 6. #26011245 | C2 | semidirect |
| 7. C2×#102×C173 | C2 | semidirect |
| 12. C2×#14583811 | C4 | semidirect |
| 32. C2×D692 | C2×C4 | semidirect |
| 42. C2×#13063436 | C2×C4 | semidirect |
| 84. C2×Dic173 | D8 | semidirect |
| 97. D4×C173 | C22⋊C4 | semidirect |
| 146. C173 | #1879 | semidirect |
| 151. C2×#102 | D173 | semidirect |
| 233. D4 | #14583803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583811 | 2 |
| C2×D4×Dic173 | 2 |
| C2×#19149601 | 2 |
| #26011392 | 2 |
| #26011253 | 2 |
| #26011245 | 2 |
| C2×#102×C173 | 2 |
| #1879 | 173 |