Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
400 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23752604 | C2 | semidirect |
| 4. #23752572 | C2 | semidirect |
| 5. #23752571 | C2 | semidirect |
| 6. #23752436 | C2 | semidirect |
| 7. #23752432 | C2 | semidirect |
| 8. #23752366 | C2 | semidirect |
| 10. #23752267 | C2 | semidirect |
| 11. #497×C151 | C2 | semidirect |
| 14. C2×#14558994 | C22 | semidirect |
| 16. #18012739 | C22 | semidirect |
| 25. Q8×Dic151 | C22 | semidirect |
| 31. Dic151⋊C8 | C22 | semidirect |
| 32. #18012664 | C22 | semidirect |
| 33. #18012663 | C22 | semidirect |
| 37. #18012650 | C22 | semidirect |
| 38. C2×Q16×C151 | C22 | semidirect |
| 40. C4⋊Q8×C151 | C22 | semidirect |
| 42. #97×C151 | C22 | semidirect |
| 142. C151 | #3215 | semidirect |
| 147. #497 | D151 | semidirect |
| 158. C2×Q16 | C2×D151 | semidirect |
| 162. C4⋊Q8 | C2×D151 | semidirect |
| 185. #97 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752767 | 2 |
| #124×D151 | 2 |
| #23752604 | 2 |
| #23752572 | 2 |
| #23752571 | 2 |
| #23752436 | 2 |
| #23752432 | 2 |
| #23752366 | 2 |
| #23752361 | 2 |
| #23752267 | 2 |
| #497×C151 | 2 |
| #3215 | 151 |