Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012769 | C2 | semidirect |
| 3. C22×#14558993 | C2 | semidirect |
| 4. #23752475 | C2 | direct (N × H) |
| 5. C2×#18012675 | C2 | semidirect |
| 6. C2×#18012657 | C2 | semidirect |
| 7. C2×#18012655 | C2 | semidirect |
| 8. C2×#131×C151 | C2 | semidirect |
| 12. #18012769 | C22 | semidirect |
| 19. C2×#14558993 | C22 | semidirect |
| 25. #18012675 | C22 | semidirect |
| 26. #18012657 | C22 | semidirect |
| 27. #18012655 | C22 | semidirect |
| 30. #131×C151 | C22 | semidirect |
| 135. C2×C151 | #471 | semidirect |
| 138. C151 | C2×#471 | semidirect |
| 143. C2×#131 | D151 | semidirect |
| 164. #131 | C2×D151 | semidirect |
| 275. C2 | #23752475 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012769 | 2 |
| C2×#18012764 | 2 |
| C22×#14558993 | 2 |
| #23752475 | 2 |
| C2×#18012675 | 2 |
| C2×#18012657 | 2 |
| C2×#18012655 | 2 |
| C2×#131×C151 | 2 |
| C2×#471 | 151 |