Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26012162 | C2 | semidirect |
| 3. #26011867 | C2 | semidirect |
| 4. #26011725 | C2 | semidirect |
| 5. #26011691 | C2 | semidirect |
| 6. #26011688 | C2 | semidirect |
| 7. #26011636 | C2 | semidirect |
| 8. #26011634 | C2 | semidirect |
| 9. C4×#14583816 | C2 | semidirect |
| 10. D4×#13063436 | C2 | semidirect |
| 11. #550×C173 | C2 | semidirect |
| 51. #14583816 | D4 | semidirect |
| 131. C4×C173 | #135 | semidirect |
| 142. C173 | #3287 | semidirect |
| 146. #550 | D173 | semidirect |
| 276. 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 |
| #26012162 | 2 |
| #26011867 | 2 |
| #26011725 | 2 |
| #26011691 | 2 |
| #26011688 | 2 |
| #26011636 | 2 |
| #26011634 | 2 |
| C4×#14583816 | 2 |
| D4×#13063436 | 2 |
| #550×C173 | 2 |
| #3287 | 173 |