Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23752759 | C2 | semidirect |
| 2. #127×D151 | C2 | semidirect |
| 3. #23752587 | C2 | semidirect |
| 4. #23752557 | C2 | semidirect |
| 5. #23752408 | C2 | semidirect |
| 6. #23752407 | C2 | semidirect |
| 7. #23752404 | C2 | semidirect |
| 8. #23752347 | C2 | semidirect |
| 9. #23752344 | C2 | semidirect |
| 10. #23752264 | C2 | semidirect |
| 11. #459×C151 | C2 | semidirect |
| 16. C2×D1208 | C22 | semidirect |
| 17. C2×#14558989 | C22 | semidirect |
| 18. C2×#14558989 | C22 | semidirect |
| 19. #18012738 | C22 | semidirect |
| 24. #18012735 | C22 | semidirect |
| 29. C4×D604 | C22 | semidirect |
| 32. C4⋊(C151⋊C8) | C22 | semidirect |
| 33. #18012661 | C22 | semidirect |
| 34. #18012660 | C22 | semidirect |
| 35. #18012659 | C22 | semidirect |
| 37. C8×Dic151 | C22 | semidirect |
| 38. C2×D8×C151 | C22 | semidirect |
| 40. C4×D4×C151 | C22 | semidirect |
| 41. C4⋊C8×C151 | C22 | semidirect |
| 42. #102×C151 | C22 | semidirect |
| 115. C4×D151 | D8 | semidirect |
| 165. C151 | #3205 | semidirect |
| 174. #459 | D151 | semidirect |
| 185. C2×D8 | C2×D151 | semidirect |
| 199. C4×D4 | C2×D151 | semidirect |
| 202. C4⋊C8 | C2×D151 | semidirect |
| 206. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752759 | 2 |
| #127×D151 | 2 |
| #23752587 | 2 |
| #23752557 | 2 |
| #23752408 | 2 |
| #23752407 | 2 |
| #23752404 | 2 |
| #23752347 | 2 |
| #23752344 | 2 |
| #23752264 | 2 |
| #459×C151 | 2 |
| #3205 | 151 |