Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
448 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23752764 | C2 | semidirect |
| 3. #23752543 | C2 | semidirect |
| 4. #23752540 | C2 | semidirect |
| 5. #23752500 | C2 | semidirect |
| 6. #23752415 | C2 | semidirect |
| 8. #23752303 | C2 | semidirect |
| 9. SD16×Dic151 | C2 | semidirect |
| 10. #23752262 | C2 | semidirect |
| 14. #18012738 | C22 | semidirect |
| 15. #18012737 | C22 | semidirect |
| 19. Q8×Dic151 | C22 | semidirect |
| 21. #18012704 | C22 | semidirect |
| 30. #18012671 | C22 | semidirect |
| 31. #18012670 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. #18012664 | C22 | semidirect |
| 34. #18012663 | C22 | semidirect |
| 37. C8×Dic151 | C22 | semidirect |
| 91. C2×Dic151 | SD16 | semidirect |
| 136. C151 | #3101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752764 | 2 |
| C2×D4×Dic151 | 2 |
| #23752543 | 2 |
| #23752540 | 2 |
| #23752500 | 2 |
| #23752415 | 2 |
| #23752363 | 2 |
| #23752303 | 2 |
| SD16×Dic151 | 2 |
| #23752262 | 2 |
| #450×C151 | 2 |
| #3101 | 151 |