Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 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. #23752743 | C2 | semidirect |
| 2. C2×#18012726 | C2 | semidirect |
| 3. #23752595 | C2 | semidirect |
| 4. #23752565 | C2 | semidirect |
| 5. #23752433 | C2 | semidirect |
| 6. #23752425 | C2 | semidirect |
| 7. #23752370 | C2 | semidirect |
| 8. #23752363 | C2 | semidirect |
| 9. #23752350 | C2 | semidirect |
| 10. #23752262 | C2 | semidirect |
| 13. C2×Dic604 | C22 | semidirect |
| 15. C2×#14558992 | C22 | semidirect |
| 17. #18012730 | C22 | semidirect |
| 22. #18012726 | C22 | semidirect |
| 25. #18012704 | C22 | semidirect |
| 27. D4×Dic151 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. #18012664 | C22 | semidirect |
| 34. #18012662 | C22 | semidirect |
| 37. C8×Dic151 | C22 | semidirect |
| 143. C151 | #3211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752743 | 2 |
| C2×#18012726 | 2 |
| #23752595 | 2 |
| #23752565 | 2 |
| #23752433 | 2 |
| #23752425 | 2 |
| #23752370 | 2 |
| #23752363 | 2 |
| #23752350 | 2 |
| #23752262 | 2 |
| #447×C151 | 2 |
| #3211 | 151 |