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. #23753020 | C2 | semidirect |
| 2. #23753014 | C2 | semidirect |
| 3. #23752597 | C2 | semidirect |
| 4. #23752484 | C2 | semidirect |
| 5. #23752482 | C2 | semidirect |
| 6. #23752477 | C2 | semidirect |
| 7. #23752388 | C2 | semidirect |
| 8. #23752385 | C2 | semidirect |
| 9. #23752329 | C2 | semidirect |
| 10. #23752327 | C2 | semidirect |
| 11. #578×C151 | C2 | semidirect |
| 18. #18012764 | C22 | semidirect |
| 23. C2×#14558991 | C22 | semidirect |
| 26. #18012746 | C22 | semidirect |
| 28. #18012728 | C22 | semidirect |
| 29. #18012675 | C22 | semidirect |
| 30. #18012674 | C22 | semidirect |
| 31. #18012666 | C22 | semidirect |
| 32. #18012666 | C22 | semidirect |
| 34. #18012658 | C22 | semidirect |
| 35. #18012655 | C22 | semidirect |
| 36. C8×Dic151 | C22 | semidirect |
| 37. 2−1+4×C151 | C22 | semidirect |
| 39. #137×C151 | C22 | semidirect |
| 43. C2×Q16×C151 | C22 | semidirect |
| 44. #131×C151 | C22 | semidirect |
| 149. C151 | #3290 | semidirect |
| 151. #578 | D151 | semidirect |
| 162. 2−1+4 | C2×D151 | semidirect |
| 167. #137 | C2×D151 | semidirect |
| 178. C2×Q16 | C2×D151 | semidirect |
| 185. #131 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23753020 | 2 |
| #23753014 | 2 |
| #23752597 | 2 |
| #23752484 | 2 |
| #23752482 | 2 |
| #23752477 | 2 |
| #23752388 | 2 |
| #23752385 | 2 |
| #23752329 | 2 |
| #23752327 | 2 |
| #578×C151 | 2 |
| #3290 | 151 |