Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #23752310 | C2 | semidirect |
| 4. C4×#14558991 | C2 | semidirect |
| 5. #23752248 | C2 | semidirect |
| 6. #23752221 | C2 | semidirect |
| 8. #23752168 | C2 | semidirect |
| 9. #519×C151 | C2 | semidirect |
| 11. C2×#14558991 | C4 | semidirect |
| 20. #18012672 | C22 | semidirect |
| 21. #18012670 | C22 | semidirect |
| 22. #18012663 | C22 | semidirect |
| 24. #18012650 | C22 | semidirect |
| 25. C4×C151⋊C8 | C22 | semidirect |
| 28. C4×Q8×C151 | C22 | semidirect |
| 38. #14558991 | C2×C4 | semidirect |
| 39. #14558991 | C2×C4 | semidirect |
| 41. C2×C151⋊C8 | C2×C4 | semidirect |
| 51. C2×Q8×C151 | C2×C4 | semidirect |
| 103. C151 | #2949 | semidirect |
| 106. #519 | D151 | semidirect |
| 122. C4×Q8 | C2×D151 | semidirect |
| 139. C2×Q8 | C4×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558991 | 2 |
| #23752686 | 2 |
| #23752310 | 2 |
| C4×#14558991 | 2 |
| #23752248 | 2 |
| #23752221 | 2 |
| #23752216 | 2 |
| #23752168 | 2 |
| #519×C151 | 2 |
| #2949 | 151 |