Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 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 |
|---|---|---|
| 2. #23752692 | C2 | semidirect |
| 3. #23752535 | C2 | semidirect |
| 4. #23752534 | C2 | semidirect |
| 5. #23752529 | C2 | semidirect |
| 6. #23752524 | C2 | semidirect |
| 7. #23752254 | C2 | semidirect |
| 8. #23752248 | C2 | semidirect |
| 9. C2×#18012660 | C2 | semidirect |
| 10. #23752180 | C2 | semidirect |
| 11. #418×C151 | C2 | semidirect |
| 23. #18012697 | C22 | semidirect |
| 25. C4⋊C4×D151 | C22 | semidirect |
| 26. #18012673 | C22 | semidirect |
| 27. #18012672 | C22 | semidirect |
| 28. #18012672 | C22 | semidirect |
| 29. #18012671 | C22 | semidirect |
| 30. #18012670 | C22 | semidirect |
| 31. #18012670 | C22 | semidirect |
| 34. (C2×D151)⋊C8 | C22 | semidirect |
| 35. (C2×D151)⋊C8 | C22 | semidirect |
| 134. C151 | #3096 | semidirect |
| 144. #418 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752779 | 2 |
| #23752692 | 2 |
| #23752535 | 2 |
| #23752534 | 2 |
| #23752529 | 2 |
| #23752524 | 2 |
| #23752254 | 2 |
| #23752248 | 2 |
| C2×#18012660 | 2 |
| #23752180 | 2 |
| #418×C151 | 2 |
| #3096 | 151 |