Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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. C2×#18012718 | C2 | semidirect |
| 3. #23752374 | C2 | semidirect |
| 4. #23752368 | C2 | semidirect |
| 5. #23752363 | C2 | semidirect |
| 6. #23752213 | C2 | semidirect |
| 7. #23752176 | C2 | semidirect |
| 9. C22×Dic302 | C22 | semidirect |
| 11. C2×#14558994 | C22 | semidirect |
| 12. C2×#14558992 | C22 | semidirect |
| 13. C2×#14558988 | C22 | semidirect |
| 17. #18012718 | C22 | semidirect |
| 18. C2×C4⋊Dic151 | C22 | semidirect |
| 21. #18012663 | C22 | semidirect |
| 22. #18012660 | C22 | semidirect |
| 24. C22⋊(C151⋊C8) | C22 | semidirect |
| 130. C22×C151 | #137 | semidirect |
| 146. C151 | #3007 | semidirect |
| 277. C22 | #18012769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012769 | 2 |
| C2×#18012718 | 2 |
| #23752374 | 2 |
| #23752368 | 2 |
| #23752363 | 2 |
| #23752213 | 2 |
| #23752176 | 2 |
| C22×#41×C151 | 2 |
| #3007 | 151 |