Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#18012767 | C2 | semidirect |
| 2. C2×#18012747 | C2 | semidirect |
| 3. #23752793 | C2 | semidirect |
| 4. #23752781 | C2 | semidirect |
| 5. #23752466 | C2 | semidirect |
| 6. #23752459 | C2 | semidirect |
| 7. #23752449 | C2 | semidirect |
| 8. #23752442 | C2 | semidirect |
| 9. #23752206 | C2 | semidirect |
| 10. C2×#18012659 | C2 | semidirect |
| 11. #428×C151 | C2 | semidirect |
| 19. C2×#14558987 | C22 | semidirect |
| 21. C2×C8×D151 | C22 | semidirect |
| 25. #18012719 | C22 | semidirect |
| 29. #18012714 | C22 | semidirect |
| 32. #18012662 | C22 | semidirect |
| 33. #18012662 | C22 | semidirect |
| 36. #18012659 | C22 | semidirect |
| 37. #18012659 | C22 | semidirect |
| 41. #107×C151 | C22 | semidirect |
| 42. #106×C151 | C22 | semidirect |
| 77. M16×C151 | D4 | semidirect |
| 151. C151 | #3062 | semidirect |
| 161. #428 | D151 | semidirect |
| 187. #107 | C2×D151 | semidirect |
| 188. #106 | C2×D151 | semidirect |
| 220. M16 | D604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012767 | 2 |
| C2×#18012747 | 2 |
| #23752793 | 2 |
| #23752781 | 2 |
| #23752466 | 2 |
| #23752459 | 2 |
| #23752449 | 2 |
| #23752442 | 2 |
| #23752206 | 2 |
| C2×#18012659 | 2 |
| #428×C151 | 2 |
| #3062 | 151 |