Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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×C4×D604 | C2 | semidirect |
| 2. #23752540 | C2 | semidirect |
| 3. #23752523 | C2 | semidirect |
| 4. #23752509 | C2 | semidirect |
| 5. #23752424 | C2 | semidirect |
| 6. #23752362 | C2 | semidirect |
| 8. #23752322 | C2 | semidirect |
| 9. #23752310 | C2 | semidirect |
| 10. #23752269 | C2 | semidirect |
| 11. #529×C151 | C2 | semidirect |
| 22. #18012672 | C22 | semidirect |
| 23. #18012670 | C22 | semidirect |
| 24. C4⋊(C151⋊C8) | C22 | semidirect |
| 25. #18012663 | C22 | semidirect |
| 26. #18012660 | C22 | semidirect |
| 31. #18012650 | C22 | semidirect |
| 33. #125×C151 | C22 | semidirect |
| 34. #124×C151 | C22 | semidirect |
| 38. C4×Q8×C151 | C22 | semidirect |
| 40. C4×D4×C151 | C22 | semidirect |
| 140. C151 | #3114 | semidirect |
| 142. #529 | D151 | semidirect |
| 158. #125 | C2×D151 | semidirect |
| 159. #124 | C2×D151 | semidirect |
| 163. C4×Q8 | C2×D151 | semidirect |
| 169. C4×D4 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D604 | 2 |
| #23752540 | 2 |
| #23752523 | 2 |
| #23752509 | 2 |
| #23752424 | 2 |
| #23752362 | 2 |
| #23752345 | 2 |
| #23752322 | 2 |
| #23752310 | 2 |
| #23752269 | 2 |
| #529×C151 | 2 |
| #3114 | 151 |