Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 1. C2×#19149704 | C2 | semidirect |
| 2. #26012055 | C2 | semidirect |
| 3. C2×#19149676 | C2 | semidirect |
| 4. #26011497 | C2 | semidirect |
| 5. C2×#19149595 | C2 | semidirect |
| 6. #26011251 | C2 | semidirect |
| 7. C2×#104×C173 | C2 | semidirect |
| 44. C2×D692 | D4 | semidirect |
| 49. #14583810 | D4 | semidirect |
| 51. C4⋊Dic173 | D4 | semidirect |
| 59. C2×Q8×C173 | D4 | semidirect |
| 61. C2×D4×C173 | D4 | semidirect |
| 69. C42×C173 | D4 | semidirect |
| 138. C173 | #2002 | semidirect |
| 143. C2×#104 | D173 | semidirect |
| 174. C2×Q8 | D692 | semidirect |
| 191. C2×D4 | D692 | semidirect |
| 208. C42 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149704 | 2 |
| #26012055 | 2 |
| C2×#19149676 | 2 |
| #26011497 | 2 |
| C2×#19149595 | 2 |
| #26011251 | 2 |
| C2×#104×C173 | 2 |
| #2002 | 173 |