Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23753012 | C2 | semidirect |
| 2. C2×#18012765 | C2 | semidirect |
| 3. C2×#18012765 | C2 | semidirect |
| 4. #23752978 | C2 | semidirect |
| 5. #23752481 | C2 | semidirect |
| 6. #23752474 | C2 | semidirect |
| 7. #23752260 | C2 | semidirect |
| 8. #23752194 | C2 | semidirect |
| 9. C2×#100×C151 | C2 | semidirect |
| 13. #18012772 | C22 | semidirect |
| 15. #18012767 | C22 | semidirect |
| 22. C2×#14558992 | C22 | semidirect |
| 24. C2×#14558989 | C22 | semidirect |
| 25. #18012747 | C22 | semidirect |
| 30. #18012674 | C22 | semidirect |
| 31. #18012657 | C22 | semidirect |
| 32. #18012655 | C22 | semidirect |
| 36. #100×C151 | C22 | semidirect |
| 147. C151 | #3068 | semidirect |
| 157. C2×#100 | D151 | semidirect |
| 184. #100 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753012 | 2 |
| C2×#18012765 | 2 |
| #23752978 | 2 |
| #23752481 | 2 |
| #23752474 | 2 |
| #23752260 | 2 |
| #23752194 | 2 |
| C2×#100×C151 | 2 |
| #3068 | 151 |