Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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. #23752978 | C2 | semidirect |
| 3. #23752333 | C2 | semidirect |
| 4. #23752328 | C2 | semidirect |
| 5. C2×#18012665 | C2 | semidirect |
| 6. M16×Dic151 | C2 | semidirect |
| 7. #430×C151 | C2 | semidirect |
| 9. #18012772 | C4 | semidirect |
| 10. #18012767 | C4 | semidirect |
| 12. #18012747 | C22 | semidirect |
| 17. #18012665 | C22 | semidirect |
| 18. #18012665 | C22 | semidirect |
| 19. #18012649 | C22 | semidirect |
| 20. C8×Dic151 | C22 | semidirect |
| 23. #108×C151 | C22 | semidirect |
| 33. Dic604 | C2×C4 | semidirect |
| 34. #14558993 | C2×C4 | semidirect |
| 35. D1208 | C2×C4 | semidirect |
| 85. C151 | #2956 | semidirect |
| 91. #430 | D151 | semidirect |
| 105. #108 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753012 | 2 |
| #23752978 | 2 |
| #23752333 | 2 |
| #23752328 | 2 |
| C2×#18012665 | 2 |
| M16×Dic151 | 2 |
| #430×C151 | 2 |
| #2956 | 151 |