Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
396 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 157 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×C4×#13063436 | C2 | semidirect |
| 3. C4×C4⋊Dic173 | C2 | semidirect |
| 4. #26011253 | C2 | semidirect |
| 9. #19149600 | C4 | direct (N × H) |
| 15. C4×D4×C173 | C4 | semidirect |
| 22. C2×#13063436 | C2×C4 | semidirect |
| 24. C4⋊Dic173 | C2×C4 | semidirect |
| 55. D4×C173 | C42 | semidirect |
| 81. C4×C173 | #102 | semidirect |
| 92. C173 | C4×#102 | semidirect |
| 103. C4×D4 | Dic173 | semidirect |
| 144. D4 | C4×Dic173 | semidirect |
| 175. C4 | #19149600 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149600 | 2 |
| C2×C4×#13063436 | 2 |
| C4×C4⋊Dic173 | 2 |
| #26011253 | 2 |
| C2×C4×D4×C173 | 2 |
| C4×#102 | 173 |