Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
492 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 492 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. #23752757 | C2 | semidirect |
| 2. C2×#18012701 | C2 | semidirect |
| 3. #23752525 | C2 | semidirect |
| 4. #23752491 | C2 | semidirect |
| 5. #23752406 | C2 | semidirect |
| 6. #23752348 | C2 | semidirect |
| 7. #23752345 | C2 | semidirect |
| 8. #23752294 | C2 | semidirect |
| 9. #23752292 | C2 | semidirect |
| 10. #23752262 | C2 | semidirect |
| 11. #480×C151 | C2 | semidirect |
| 17. #18012738 | C22 | semidirect |
| 18. #18012735 | C22 | semidirect |
| 22. D4×Dic151 | C22 | semidirect |
| 27. #18012701 | C22 | semidirect |
| 31. #18012672 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 35. #18012659 | C22 | semidirect |
| 37. C8×Dic151 | C22 | semidirect |
| 40. #107×C151 | C22 | semidirect |
| 41. #102×C151 | C22 | semidirect |
| 92. D604 | #41 | semidirect |
| 99. C2×Dic151 | D8 | semidirect |
| 149. C151 | #3100 | semidirect |
| 154. #480 | D151 | semidirect |
| 184. #107 | C2×D151 | semidirect |
| 189. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752757 | 2 |
| C2×#18012701 | 2 |
| #23752525 | 2 |
| #23752491 | 2 |
| #23752406 | 2 |
| #23752348 | 2 |
| #23752345 | 2 |
| #23752294 | 2 |
| #23752292 | 2 |
| #23752262 | 2 |
| #480×C151 | 2 |
| #3100 | 151 |