Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 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. #23752764 | C2 | semidirect |
| 3. #23752583 | C2 | semidirect |
| 4. #23752557 | C2 | semidirect |
| 5. #23752411 | C2 | semidirect |
| 6. #23752410 | C2 | semidirect |
| 7. #23752365 | C2 | semidirect |
| 8. #23752363 | C2 | semidirect |
| 9. #23752362 | C2 | semidirect |
| 10. #23752262 | C2 | semidirect |
| 11. #450×C151 | C2 | semidirect |
| 15. C2×#14558993 | C22 | semidirect |
| 16. C2×#14558992 | C22 | semidirect |
| 17. C2×#14558991 | C22 | semidirect |
| 18. #18012738 | C22 | semidirect |
| 19. #18012737 | C22 | semidirect |
| 27. Q8×Dic151 | C22 | semidirect |
| 29. #18012704 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. #18012661 | C22 | semidirect |
| 34. #18012660 | C22 | semidirect |
| 35. #18012659 | C22 | semidirect |
| 37. C8×Dic151 | C22 | semidirect |
| 39. C2×SD16×C151 | C22 | semidirect |
| 41. #102×C151 | C22 | semidirect |
| 102. C2×Dic151 | SD16 | semidirect |
| 151. C151 | #3208 | semidirect |
| 162. #450 | D151 | semidirect |
| 171. C2×SD16 | 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 |
|---|---|
| #23752764 | 2 |
| C2×#18012735 | 2 |
| #23752583 | 2 |
| #23752557 | 2 |
| #23752411 | 2 |
| #23752410 | 2 |
| #23752365 | 2 |
| #23752363 | 2 |
| #23752362 | 2 |
| #23752262 | 2 |
| #450×C151 | 2 |
| #3208 | 151 |