Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
616 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 2. C2×C4×D604 | C2 | semidirect |
| 3. C4×#14558989 | C2 | direct (N × H) |
| 4. C2×#18012672 | C2 | semidirect |
| 5. C2×#18012660 | C2 | semidirect |
| 6. C2×#18012659 | C2 | semidirect |
| 7. C2×C4×C151⋊C8 | C2 | semidirect |
| 8. C2×C4×D4×C151 | C2 | semidirect |
| 11. C2×#14558989 | C4 | direct (N × H) |
| 16. C4×D604 | C22 | semidirect |
| 19. #18012672 | C22 | semidirect |
| 20. #18012660 | C22 | semidirect |
| 21. #18012659 | C22 | semidirect |
| 22. C4×C151⋊C8 | C22 | semidirect |
| 26. C4×D4×C151 | C22 | semidirect |
| 33. C2×D604 | C2×C4 | semidirect |
| 38. #14558989 | C2×C4 | direct (N × H) |
| 40. C2×C151⋊C8 | C2×C4 | semidirect |
| 49. C2×D4×C151 | C2×C4 | semidirect |
| 68. D604 | C22×C4 | semidirect |
| 73. C151⋊C8 | C22×C4 | semidirect |
| 81. D4×C151 | C22×C4 | semidirect |
| 86. C2×C4×C151 | D8 | semidirect |
| 108. C4×C151 | C2×D8 | semidirect |
| 113. C2×C151 | C4×D8 | semidirect |
| 118. C151 | C2×C4×D8 | semidirect |
| 122. C2×C4×D4 | D151 | semidirect |
| 139. C4×D4 | C2×D151 | semidirect |
| 157. C2×D4 | C4×D151 | semidirect |
| 195. D4 | C2×C4×D151 | semidirect |
| 203. C2×C4 | #14558989 | direct (N × H) |
| 228. C4 | C2×#14558989 | direct (N × H) |
| 233. C2 | C4×#14558989 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558989 | 2 |
| C2×C4×D604 | 2 |
| C4×#14558989 | 2 |
| C2×#18012672 | 2 |
| C2×#18012660 | 2 |
| C2×#18012659 | 2 |
| C2×C4×C151⋊C8 | 2 |
| C2×C4×D4×C151 | 2 |
| C2×C4×D8 | 151 |