Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#18012765 | C2 | semidirect |
| 2. #23752779 | C2 | semidirect |
| 3. #23752687 | C2 | semidirect |
| 4. #23752425 | C2 | semidirect |
| 5. #23752405 | C2 | semidirect |
| 6. #23752238 | C2 | semidirect |
| 7. #23752217 | C2 | semidirect |
| 8. #23752209 | C2 | semidirect |
| 9. C22×D8×C151 | C2 | semidirect |
| 12. C2×#14558992 | C22 | semidirect |
| 13. C2×#14558989 | C22 | semidirect |
| 15. #18012735 | C22 | semidirect |
| 16. #18012726 | C22 | semidirect |
| 20. D4×Dic151 | C22 | semidirect |
| 24. Dic151⋊C8 | C22 | semidirect |
| 25. #18012664 | C22 | semidirect |
| 26. #18012661 | C22 | semidirect |
| 27. #18012660 | C22 | semidirect |
| 60. C2×D4×C151 | D4 | semidirect |
| 121. C151 | #3041 | semidirect |
| 124. C22×D8 | D151 | semidirect |
| 168. C2×D4 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012765 | 2 |
| #23752779 | 2 |
| #23752687 | 2 |
| #23752425 | 2 |
| #23752405 | 2 |
| #23752238 | 2 |
| #23752217 | 2 |
| #23752209 | 2 |
| C22×D8×C151 | 2 |
| #3041 | 151 |