Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#18012786 | C2 | semidirect |
| 2. #23753012 | C2 | semidirect |
| 3. #23753010 | C2 | semidirect |
| 4. #23752788 | C2 | semidirect |
| 5. #23752396 | C2 | semidirect |
| 6. #23752386 | C2 | semidirect |
| 7. #23752230 | C2 | semidirect |
| 8. C2×#18012657 | C2 | semidirect |
| 9. #421×C151 | C2 | semidirect |
| 23. #18012772 | C22 | semidirect |
| 25. #18012769 | C22 | semidirect |
| 27. #18012767 | C22 | semidirect |
| 29. #18012764 | C22 | semidirect |
| 33. #18012739 | C22 | semidirect |
| 34. #18012727 | C22 | semidirect |
| 37. #18012667 | C22 | semidirect |
| 38. #18012657 | C22 | semidirect |
| 42. #104×C151 | C22 | semidirect |
| 185. C151 | #3020 | semidirect |
| 194. #421 | D151 | semidirect |
| 227. #104 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012786 | 2 |
| #23753012 | 2 |
| #23753010 | 2 |
| #23752788 | 2 |
| #23752396 | 2 |
| #23752386 | 2 |
| #23752230 | 2 |
| C2×#18012657 | 2 |
| #421×C151 | 2 |
| #3020 | 151 |