Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
444 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23752757 | C2 | semidirect |
| 2. C2×#18012728 | C2 | semidirect |
| 3. #23752598 | C2 | semidirect |
| 4. #23752573 | C2 | semidirect |
| 5. #23752430 | C2 | semidirect |
| 6. #23752429 | C2 | semidirect |
| 7. #23752351 | C2 | semidirect |
| 8. #23752348 | C2 | semidirect |
| 9. #23752345 | C2 | semidirect |
| 10. #23752266 | C2 | semidirect |
| 11. #448×C151 | C2 | semidirect |
| 14. C2×#14558991 | C22 | semidirect |
| 17. #18012738 | C22 | semidirect |
| 18. #18012735 | C22 | semidirect |
| 26. D4×Dic151 | C22 | semidirect |
| 27. #18012701 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. #18012663 | C22 | semidirect |
| 37. #18012649 | C22 | semidirect |
| 39. C2×SD16×C151 | C22 | semidirect |
| 41. #103×C151 | C22 | semidirect |
| 152. C151 | #3213 | semidirect |
| 161. #448 | D151 | semidirect |
| 169. C2×SD16 | C2×D151 | semidirect |
| 190. #103 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752757 | 2 |
| C2×#18012728 | 2 |
| #23752598 | 2 |
| #23752573 | 2 |
| #23752430 | 2 |
| #23752429 | 2 |
| #23752351 | 2 |
| #23752348 | 2 |
| #23752345 | 2 |
| #23752266 | 2 |
| #448×C151 | 2 |
| #3213 | 151 |