Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#18012764 | C2 | semidirect |
| 2. C22×D1208 | C2 | semidirect |
| 3. #23752776 | C2 | semidirect |
| 4. #23752686 | C2 | semidirect |
| 5. #23752430 | C2 | semidirect |
| 6. #23752406 | C2 | semidirect |
| 7. #23752238 | C2 | semidirect |
| 8. #23752216 | C2 | semidirect |
| 9. #416×C151 | C2 | semidirect |
| 13. C2×#14558991 | C22 | semidirect |
| 16. C2×#14558989 | C22 | semidirect |
| 18. #18012735 | C22 | semidirect |
| 19. #18012728 | C22 | semidirect |
| 23. #18012701 | C22 | semidirect |
| 26. Dic151⋊C8 | C22 | semidirect |
| 27. #18012659 | C22 | semidirect |
| 31. #103×C151 | C22 | semidirect |
| 32. #102×C151 | C22 | semidirect |
| 40. C2×D604 | D4 | semidirect |
| 121. C151 | #3041 | semidirect |
| 131. #416 | D151 | semidirect |
| 152. #103 | C2×D151 | semidirect |
| 154. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012764 | 2 |
| C22×D1208 | 2 |
| #23752776 | 2 |
| #23752686 | 2 |
| #23752430 | 2 |
| #23752406 | 2 |
| #23752238 | 2 |
| #23752216 | 2 |
| #416×C151 | 2 |
| #3041 | 151 |