Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
468 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 137 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×#18012718 | C2 | semidirect |
| 2. #23752542 | C2 | semidirect |
| 3. #23752528 | C2 | semidirect |
| 4. #23752439 | C2 | semidirect |
| 5. #23752363 | C2 | semidirect |
| 6. #23752350 | C2 | semidirect |
| 7. C2×C22⋊(C151⋊C8) | C2 | semidirect |
| 9. C22×Dic302 | C22 | semidirect |
| 10. C2×#14558992 | C22 | semidirect |
| 11. C22×C151⋊C8 | C22 | semidirect |
| 15. #18012718 | C22 | semidirect |
| 16. C2×C4⋊Dic151 | C22 | semidirect |
| 19. #18012670 | C22 | semidirect |
| 20. #18012662 | C22 | semidirect |
| 21. #18012660 | C22 | semidirect |
| 23. C22⋊(C151⋊C8) | C22 | semidirect |
| 80. C23×C151 | SD16 | semidirect |
| 129. C151 | #3187 | semidirect |
| 203. C23 | #14558992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012718 | 2 |
| #23752542 | 2 |
| #23752528 | 2 |
| #23752439 | 2 |
| #23752363 | 2 |
| #23752350 | 2 |
| C2×C22⋊(C151⋊C8) | 2 |
| C2×#121×C151 | 2 |
| #3187 | 151 |