Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#18012758 | C2 | semidirect |
| 2. #23752856 | C2 | semidirect |
| 3. #23752595 | C2 | semidirect |
| 4. #23752453 | C2 | semidirect |
| 5. #23752445 | C2 | semidirect |
| 6. #23752425 | C2 | semidirect |
| 7. #23752363 | C2 | semidirect |
| 8. #23752354 | C2 | semidirect |
| 9. D8×Dic151 | C2 | semidirect |
| 10. C8×C22⋊D151 | C2 | semidirect |
| 11. C22×D8×C151 | C2 | semidirect |
| 12. C2×#14559003 | C22 | semidirect |
| 14. C2×Dic604 | C22 | semidirect |
| 15. C2×#14558992 | C22 | semidirect |
| 16. C2×#14558992 | C22 | semidirect |
| 17. C2×C8×D151 | C22 | semidirect |
| 18. #18012726 | C22 | semidirect |
| 22. #18012710 | C22 | semidirect |
| 24. D4×Dic151 | C22 | semidirect |
| 27. #18012673 | C22 | semidirect |
| 28. Dic151⋊C8 | C22 | semidirect |
| 29. #18012664 | C22 | semidirect |
| 30. #18012660 | C22 | semidirect |
| 31. #18012660 | C22 | semidirect |
| 33. (C2×D151)⋊C8 | C22 | semidirect |
| 34. C8×Dic151 | C22 | semidirect |
| 76. D8×C151 | D4 | semidirect |
| 123. C22×C151 | #135 | semidirect |
| 143. C151 | #3280 | semidirect |
| 146. C22×D8 | D151 | semidirect |
| 206. D8 | C22⋊D151 | semidirect |
| 270. C22 | #18012758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012758 | 2 |
| #23752856 | 2 |
| #23752595 | 2 |
| #23752453 | 2 |
| #23752445 | 2 |
| #23752425 | 2 |
| #23752363 | 2 |
| #23752354 | 2 |
| D8×Dic151 | 2 |
| C8×C22⋊D151 | 2 |
| C22×D8×C151 | 2 |
| #3280 | 151 |