Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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. #23753026 | C2 | semidirect |
| 2. #23753024 | C2 | semidirect |
| 3. #23753014 | C2 | semidirect |
| 4. #23752596 | C2 | semidirect |
| 5. #23752488 | C2 | semidirect |
| 6. #23752483 | C2 | semidirect |
| 7. #23752475 | C2 | semidirect |
| 8. #23752391 | C2 | semidirect |
| 9. #23752386 | C2 | semidirect |
| 10. #23752330 | C2 | semidirect |
| 11. #443×C151 | C2 | semidirect |
| 12. #18012786 | C22 | semidirect |
| 16. #18012769 | C22 | semidirect |
| 19. #18012767 | C22 | semidirect |
| 26. C2×Dic604 | C22 | semidirect |
| 29. C2×#14558993 | C22 | semidirect |
| 33. #18012745 | C22 | semidirect |
| 34. #18012727 | C22 | semidirect |
| 35. #18012675 | C22 | semidirect |
| 37. #18012667 | C22 | semidirect |
| 38. #18012657 | C22 | semidirect |
| 39. #18012655 | C22 | semidirect |
| 41. #131×C151 | C22 | semidirect |
| 42. #108×C151 | C22 | semidirect |
| 43. #104×C151 | C22 | semidirect |
| 44. C4×C8×C151 | C22 | semidirect |
| 149. C151 | #3290 | semidirect |
| 161. #443 | D151 | semidirect |
| 185. #131 | C2×D151 | semidirect |
| 188. #108 | C2×D151 | semidirect |
| 191. #104 | C2×D151 | semidirect |
| 194. C4×C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753026 | 2 |
| #23753024 | 2 |
| #23753014 | 2 |
| #23752596 | 2 |
| #23752488 | 2 |
| #23752483 | 2 |
| #23752475 | 2 |
| #23752391 | 2 |
| #23752386 | 2 |
| #23752330 | 2 |
| #443×C151 | 2 |
| #3290 | 151 |