Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 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. #23752746 | C2 | semidirect |
| 2. C2×C4×D604 | C2 | semidirect |
| 3. #23752543 | C2 | semidirect |
| 4. #23752526 | C2 | semidirect |
| 5. #23752513 | C2 | semidirect |
| 6. #23752428 | C2 | semidirect |
| 7. #23752365 | C2 | semidirect |
| 9. #23752325 | C2 | semidirect |
| 10. #23752314 | C2 | semidirect |
| 11. #432×C151 | C2 | semidirect |
| 17. #18012731 | C22 | semidirect |
| 18. #18012727 | C22 | semidirect |
| 22. C4×Dic302 | C22 | semidirect |
| 27. C4×D604 | C22 | semidirect |
| 32. #18012673 | C22 | semidirect |
| 33. #18012671 | C22 | semidirect |
| 34. #18012664 | C22 | semidirect |
| 37. #18012661 | C22 | semidirect |
| 39. C4⋊C8×C151 | C22 | semidirect |
| 42. #97×C151 | C22 | semidirect |
| 140. C151 | #3114 | semidirect |
| 152. #432 | D151 | semidirect |
| 176. C4⋊C8 | C2×D151 | semidirect |
| 183. #97 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752746 | 2 |
| C2×C4×D604 | 2 |
| #23752543 | 2 |
| #23752526 | 2 |
| #23752513 | 2 |
| #23752428 | 2 |
| #23752365 | 2 |
| #23752348 | 2 |
| #23752325 | 2 |
| #23752314 | 2 |
| #432×C151 | 2 |
| #3114 | 151 |