Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23752767 | C2 | semidirect |
| 3. #23752585 | C2 | semidirect |
| 4. #23752584 | C2 | semidirect |
| 5. #23752560 | C2 | semidirect |
| 6. #23752411 | C2 | semidirect |
| 7. #23752364 | C2 | semidirect |
| 8. #23752263 | C2 | semidirect |
| 9. #486×C151 | C2 | semidirect |
| 13. C2×#14558993 | C22 | semidirect |
| 14. C2×#14558992 | C22 | semidirect |
| 15. #18012739 | C22 | semidirect |
| 24. #18012704 | C22 | semidirect |
| 27. Dic151⋊C8 | C22 | semidirect |
| 28. #18012659 | C22 | semidirect |
| 30. C4×C151⋊C8 | C22 | semidirect |
| 31. C4⋊Q8×C151 | C22 | semidirect |
| 33. #102×C151 | C22 | semidirect |
| 34. C4×C8×C151 | C22 | semidirect |
| 87. C4×D151 | SD16 | semidirect |
| 124. C151 | #3208 | semidirect |
| 131. #486 | D151 | semidirect |
| 141. C4⋊Q8 | C2×D151 | semidirect |
| 156. #102 | C2×D151 | semidirect |
| 159. C4×C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752767 | 2 |
| #127×D151 | 2 |
| #23752585 | 2 |
| #23752584 | 2 |
| #23752560 | 2 |
| #23752411 | 2 |
| #23752364 | 2 |
| #23752263 | 2 |
| #486×C151 | 2 |
| #3208 | 151 |