Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #23753010 | C2 | semidirect |
| 2. C2×#18012765 | C2 | semidirect |
| 3. #23752978 | C2 | semidirect |
| 4. #23752479 | C2 | semidirect |
| 5. #23752472 | C2 | semidirect |
| 6. #23752261 | C2 | semidirect |
| 7. #23752196 | C2 | semidirect |
| 8. C2×#18012656 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C151 | C2 | semidirect |
| 11. #18012770 | C22 | semidirect |
| 15. #18012765 | C22 | semidirect |
| 21. #18012745 | C22 | semidirect |
| 26. #18012675 | C22 | semidirect |
| 27. #18012658 | C22 | semidirect |
| 28. #18012656 | C22 | semidirect |
| 29. #18012656 | C22 | semidirect |
| 34. C2×SD16×C151 | C22 | semidirect |
| 35. C2×D8×C151 | C22 | semidirect |
| 147. C151 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D151 | semidirect |
| 171. C2×SD16 | C2×D151 | semidirect |
| 173. C2×D8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753010 | 2 |
| C2×#18012765 | 2 |
| #23752978 | 2 |
| #23752479 | 2 |
| #23752472 | 2 |
| #23752261 | 2 |
| #23752196 | 2 |
| C2×#18012656 | 2 |
| C2×AGL(1,ℤ/8)×C151 | 2 |
| #3068 | 151 |