Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#18012759 | C2 | semidirect |
| 2. #23752779 | C2 | semidirect |
| 3. #23752695 | C2 | semidirect |
| 4. #23752432 | C2 | semidirect |
| 5. #23752425 | C2 | semidirect |
| 6. #23752410 | C2 | semidirect |
| 7. #23752405 | C2 | semidirect |
| 8. #23752240 | C2 | semidirect |
| 9. #23752214 | C2 | semidirect |
| 10. C2×#18012660 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C151 | C2 | semidirect |
| 14. C2×#14558994 | C22 | semidirect |
| 15. C2×#14558992 | C22 | semidirect |
| 16. C2×#14558991 | C22 | semidirect |
| 17. C2×#14558989 | C22 | semidirect |
| 24. Q8×Dic151 | C22 | semidirect |
| 26. D4×Dic151 | C22 | semidirect |
| 31. Dic151⋊C8 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. #18012664 | C22 | semidirect |
| 34. #18012661 | C22 | semidirect |
| 73. #41×C151 | D4 | semidirect |
| 154. C151 | #3045 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D151 | semidirect |
| 202. #41 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012759 | 2 |
| #23752779 | 2 |
| #23752695 | 2 |
| #23752432 | 2 |
| #23752425 | 2 |
| #23752410 | 2 |
| #23752405 | 2 |
| #23752240 | 2 |
| #23752214 | 2 |
| C2×#18012660 | 2 |
| C2×AGL(1,ℤ/8)×C151 | 2 |
| #3045 | 151 |