Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 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. #23752923 | C2 | semidirect |
| 3. #23752560 | C2 | semidirect |
| 4. #23752532 | C2 | semidirect |
| 5. #23752442 | C2 | semidirect |
| 6. #23752413 | C2 | semidirect |
| 7. #23752364 | C2 | semidirect |
| 8. C4×#14558992 | C2 | semidirect |
| 9. #23752277 | C2 | semidirect |
| 10. #102×D151 | C2 | semidirect |
| 11. #476×C151 | C2 | semidirect |
| 14. C2×#14558993 | C22 | semidirect |
| 16. C2×C8×D151 | C22 | semidirect |
| 19. #18012719 | C22 | semidirect |
| 24. C4×Dic302 | C22 | semidirect |
| 27. C4⋊C4×D151 | C22 | semidirect |
| 28. #18012670 | C22 | semidirect |
| 29. #18012662 | C22 | semidirect |
| 30. #18012661 | C22 | semidirect |
| 32. #18012659 | C22 | semidirect |
| 33. #18012659 | C22 | semidirect |
| 34. (C2×D151)⋊C8 | C22 | semidirect |
| 35. C4×C151⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C151 | C22 | semidirect |
| 38. #106×C151 | C22 | semidirect |
| 39. C4⋊C8×C151 | C22 | semidirect |
| 89. D604 | SD16 | semidirect |
| 136. C151 | #3295 | semidirect |
| 142. #476 | D151 | semidirect |
| 154. C4⋊Q8 | C2×D151 | semidirect |
| 168. #106 | C2×D151 | semidirect |
| 169. C4⋊C8 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752923 | 2 |
| D4×D604 | 2 |
| #23752560 | 2 |
| #23752532 | 2 |
| #23752442 | 2 |
| #23752413 | 2 |
| #23752364 | 2 |
| C4×#14558992 | 2 |
| #23752277 | 2 |
| #102×D151 | 2 |
| #476×C151 | 2 |
| #3295 | 151 |