Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23752762 | C2 | semidirect |
| 2. #23752602 | C2 | semidirect |
| 3. #23752571 | C2 | semidirect |
| 4. #23752424 | C2 | semidirect |
| 5. #23752351 | C2 | semidirect |
| 6. #23752346 | C2 | semidirect |
| 7. #23752269 | C2 | semidirect |
| 8. C2×#124×C151 | C2 | semidirect |
| 10. C2×#14558991 | C22 | semidirect |
| 12. #18012739 | C22 | semidirect |
| 13. #18012736 | C22 | semidirect |
| 18. C4×D604 | C22 | semidirect |
| 19. C4⋊(C151⋊C8) | C22 | semidirect |
| 20. #18012663 | C22 | semidirect |
| 23. #18012650 | C22 | semidirect |
| 120. C151 | #3213 | semidirect |
| 123. C2×#124 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752762 | 2 |
| #23752602 | 2 |
| #23752571 | 2 |
| #23752424 | 2 |
| #23752351 | 2 |
| #23752346 | 2 |
| #23752269 | 2 |
| C2×#124×C151 | 2 |
| #3213 | 151 |