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. #23752757 | C2 | semidirect |
| 2. C2×#18012735 | C2 | semidirect |
| 3. #23752587 | C2 | semidirect |
| 4. #23752557 | C2 | semidirect |
| 5. #23752406 | C2 | semidirect |
| 6. #23752405 | C2 | semidirect |
| 7. #23752348 | C2 | semidirect |
| 8. #23752346 | C2 | semidirect |
| 9. #23752345 | C2 | semidirect |
| 10. #23752262 | C2 | semidirect |
| 11. #447×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 |
| 28. D4×Dic151 | C22 | semidirect |
| 29. #18012701 | 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×D8×C151 | C22 | semidirect |
| 41. #102×C151 | C22 | semidirect |
| 107. C2×Dic151 | D8 | semidirect |
| 164. C151 | #3205 | semidirect |
| 175. #447 | D151 | semidirect |
| 185. C2×D8 | C2×D151 | semidirect |
| 204. #102 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752757 | 2 |
| C2×#18012735 | 2 |
| #23752587 | 2 |
| #23752557 | 2 |
| #23752406 | 2 |
| #23752405 | 2 |
| #23752348 | 2 |
| #23752346 | 2 |
| #23752345 | 2 |
| #23752262 | 2 |
| #447×C151 | 2 |
| #3205 | 151 |