Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
1344 conjugacy classes of subgroups; only the 469 normal subgroups are shown.
This group has 1344 conjugacy classes of subgroups — too many to draw. Only its 469 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. #23752949 | C2 | direct (N × H) |
| 2. C2×#18012733 | C2 | semidirect |
| 3. C2×#18012720 | C2 | semidirect |
| 4. C2×#18012711 | C2 | semidirect |
| 5. C2×#18012707 | C2 | semidirect |
| 6. C2×#127×C151 | C2 | semidirect |
| 9. C23×Dic151 | C22 | semidirect |
| 10. #18012733 | C22 | semidirect |
| 11. #18012720 | C22 | semidirect |
| 12. #18012711 | C22 | semidirect |
| 13. #18012707 | C22 | semidirect |
| 14. C2×Dic151⋊C4 | C22 | semidirect |
| 16. C2×C22⋊Dic151 | C22 | semidirect |
| 19. C22×D4×C151 | C22 | semidirect |
| 20. #127×C151 | C22 | semidirect |
| 21. C2×C42×C151 | C22 | semidirect |
| 29. C22×Dic151 | C23 | semidirect |
| 30. Dic151⋊C4 | C23 | semidirect |
| 32. C22⋊Dic151 | C23 | semidirect |
| 39. C2×D4×C151 | C23 | semidirect |
| 41. C42×C151 | C23 | semidirect |
| 74. C2×C151 | #560 | semidirect |
| 77. C151 | C2×#560 | semidirect |
| 80. C2×#127 | D151 | semidirect |
| 88. C22×D4 | C2×D151 | semidirect |
| 90. #127 | C2×D151 | semidirect |
| 99. C2×C42 | C2×D151 | semidirect |
| 110. C2×D4 | C22×D151 | semidirect |
| 119. C42 | C22×D151 | semidirect |
| 153. C2 | #23752949 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752949 | 2 |
| C2×#18012733 | 2 |
| C2×#18012720 | 2 |
| C2×#18012711 | 2 |
| C2×#18012707 | 2 |
| C2×#127×C151 | 2 |
| C2×#560 | 151 |