Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
752 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 165 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×#18012769 | C2 | semidirect |
| 2. C22×#14558992 | C2 | semidirect |
| 3. #23752783 | C2 | semidirect |
| 4. #23752374 | C2 | semidirect |
| 5. #23752363 | C2 | semidirect |
| 6. #23752217 | C2 | semidirect |
| 7. #23752208 | C2 | semidirect |
| 8. #23752179 | C2 | semidirect |
| 10. C22×Dic302 | C22 | semidirect |
| 12. C2×#14558994 | C22 | semidirect |
| 14. C2×#14558992 | C22 | semidirect |
| 15. C2×#14558992 | C22 | semidirect |
| 16. C2×#14558988 | C22 | semidirect |
| 17. C22×C151⋊C8 | C22 | semidirect |
| 21. #18012718 | C22 | semidirect |
| 22. #18012698 | C22 | semidirect |
| 23. #18012663 | C22 | semidirect |
| 24. #18012660 | C22 | semidirect |
| 25. #18012660 | C22 | semidirect |
| 26. C22⋊(C151⋊C8) | C22 | semidirect |
| 146. C151 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012769 | 2 |
| C22×#14558992 | 2 |
| #23752783 | 2 |
| #23752374 | 2 |
| #23752363 | 2 |
| #23752217 | 2 |
| #23752208 | 2 |
| #23752179 | 2 |
| C2×H(5,𝔽2)×C151 | 2 |
| #3009 | 151 |