Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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×D8×D151 | C2 | semidirect |
| 2. C2×#18012745 | C2 | semidirect |
| 3. #23752778 | C2 | semidirect |
| 4. #23752464 | C2 | semidirect |
| 5. #23752463 | C2 | semidirect |
| 6. #23752449 | C2 | semidirect |
| 7. #23752448 | C2 | semidirect |
| 8. #23752445 | C2 | semidirect |
| 9. #23752249 | C2 | semidirect |
| 10. #23752215 | C2 | semidirect |
| 11. #466×C151 | C2 | semidirect |
| 18. C2×#14558988 | C22 | semidirect |
| 20. C2×#14558987 | C22 | semidirect |
| 22. C2×C8×D151 | C22 | semidirect |
| 25. #18012714 | C22 | semidirect |
| 26. #18012713 | C22 | semidirect |
| 27. #18012710 | C22 | semidirect |
| 31. #18012673 | C22 | semidirect |
| 32. #18012670 | C22 | semidirect |
| 33. #18012661 | C22 | semidirect |
| 34. #18012660 | C22 | semidirect |
| 35. #18012659 | C22 | semidirect |
| 37. C22×C8×C151 | C22 | semidirect |
| 38. #121×C151 | C22 | semidirect |
| 39. #107×C151 | C22 | semidirect |
| 40. #102×C151 | C22 | semidirect |
| 65. C8×D151 | D4 | semidirect |
| 150. C151 | #3058 | semidirect |
| 160. #466 | D151 | semidirect |
| 175. C22×C8 | C2×D151 | semidirect |
| 181. #121 | C2×D151 | semidirect |
| 186. #107 | C2×D151 | semidirect |
| 191. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D151 | 2 |
| C2×#18012745 | 2 |
| #23752778 | 2 |
| #23752464 | 2 |
| #23752463 | 2 |
| #23752449 | 2 |
| #23752448 | 2 |
| #23752445 | 2 |
| #23752249 | 2 |
| #23752215 | 2 |
| #466×C151 | 2 |
| #3058 | 151 |