Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 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×#18012698 | C2 | semidirect |
| 2. #23752533 | C2 | semidirect |
| 3. #23752528 | C2 | semidirect |
| 4. #23752523 | C2 | semidirect |
| 5. #23752252 | C2 | semidirect |
| 6. #23752217 | C2 | semidirect |
| 7. #23752176 | C2 | semidirect |
| 13. #18012698 | C22 | semidirect |
| 14. C2×C4⋊Dic151 | C22 | semidirect |
| 15. C2×C4⋊Dic151 | C22 | semidirect |
| 18. #18012672 | C22 | semidirect |
| 19. #18012670 | C22 | semidirect |
| 20. #18012660 | C22 | semidirect |
| 21. #18012660 | C22 | semidirect |
| 22. C22⋊(C151⋊C8) | C22 | semidirect |
| 23. C22⋊(C151⋊C8) | C22 | semidirect |
| 125. C151 | #3094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012698 | 2 |
| #23752533 | 2 |
| #23752528 | 2 |
| #23752523 | 2 |
| #23752252 | 2 |
| #23752217 | 2 |
| #23752176 | 2 |
| C2×#121×C151 | 2 |
| #3094 | 151 |