Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×#18012715 | C2 | semidirect |
| 3. #23752552 | C2 | semidirect |
| 4. #23752548 | C2 | semidirect |
| 5. #23752528 | C2 | semidirect |
| 6. #23752469 | C2 | semidirect |
| 7. #23752455 | C2 | semidirect |
| 8. #23752371 | C2 | semidirect |
| 9. #23752368 | C2 | semidirect |
| 10. #23752174 | C2 | semidirect |
| 11. #448×C151 | C2 | semidirect |
| 14. C2×#14558994 | C22 | semidirect |
| 31. #18012673 | C22 | semidirect |
| 32. #18012670 | C22 | semidirect |
| 33. #18012664 | C22 | semidirect |
| 34. #18012663 | C22 | semidirect |
| 35. #18012660 | C22 | semidirect |
| 39. C2×SD16×C151 | C22 | semidirect |
| 41. #103×C151 | C22 | semidirect |
| 149. C151 | #3196 | semidirect |
| 160. #448 | D151 | semidirect |
| 166. C2×SD16 | C2×D151 | semidirect |
| 188. #103 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752722 | 2 |
| C2×#18012715 | 2 |
| #23752552 | 2 |
| #23752548 | 2 |
| #23752528 | 2 |
| #23752469 | 2 |
| #23752455 | 2 |
| #23752371 | 2 |
| #23752368 | 2 |
| #23752174 | 2 |
| #448×C151 | 2 |
| #3196 | 151 |