Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
572 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 572 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 |
|---|---|---|
| 1. C2×#19149699 | C2 | semidirect |
| 2. #26012041 | C2 | semidirect |
| 3. #26011873 | C2 | semidirect |
| 4. #26011870 | C2 | semidirect |
| 5. #26011867 | C2 | semidirect |
| 6. #26011865 | C2 | semidirect |
| 7. #26011863 | C2 | semidirect |
| 8. C2×C4×#13063436 | C2 | semidirect |
| 9. #532×C173 | C2 | semidirect |
| 42. C2×#13063436 | D4 | semidirect |
| 93. C4×C173 | #135 | semidirect |
| 101. C173 | #3147 | semidirect |
| 105. #532 | D173 | semidirect |
| 196. C4 | #19149699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149699 | 2 |
| #26012041 | 2 |
| #26011873 | 2 |
| #26011870 | 2 |
| #26011867 | 2 |
| #26011865 | 2 |
| #26011863 | 2 |
| C2×C4×#13063436 | 2 |
| #532×C173 | 2 |
| #3147 | 173 |