Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
450 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23752746 | C2 | semidirect |
| 2. #23752542 | C2 | semidirect |
| 3. #23752525 | C2 | semidirect |
| 4. #23752512 | C2 | semidirect |
| 5. #23752427 | C2 | semidirect |
| 6. #23752363 | C2 | semidirect |
| 8. #23752322 | C2 | semidirect |
| 9. #23752312 | C2 | semidirect |
| 10. #23752269 | C2 | semidirect |
| 11. C2×C4×D4×C151 | C2 | semidirect |
| 15. #18012731 | C22 | semidirect |
| 16. #18012727 | C22 | semidirect |
| 20. C4×Dic302 | C22 | semidirect |
| 21. C4×D604 | C22 | semidirect |
| 24. #18012672 | C22 | semidirect |
| 25. #18012670 | C22 | semidirect |
| 26. C4⋊(C151⋊C8) | C22 | semidirect |
| 27. #18012662 | C22 | semidirect |
| 30. #18012659 | C22 | semidirect |
| 33. #18012650 | C22 | semidirect |
| 140. C151 | #3114 | semidirect |
| 143. C2×C4×D4 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752746 | 2 |
| #23752542 | 2 |
| #23752525 | 2 |
| #23752512 | 2 |
| #23752427 | 2 |
| #23752363 | 2 |
| #23752346 | 2 |
| #23752322 | 2 |
| #23752312 | 2 |
| #23752269 | 2 |
| C2×C4×D4×C151 | 2 |
| #3114 | 151 |