Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
448 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23752542 | C2 | semidirect |
| 4. #23752501 | C2 | semidirect |
| 5. #23752416 | C2 | semidirect |
| 8. #23752299 | C2 | semidirect |
| 9. #23752297 | C2 | semidirect |
| 10. #23752262 | C2 | semidirect |
| 11. #483×C151 | C2 | semidirect |
| 16. #18012738 | C22 | semidirect |
| 17. #18012737 | C22 | semidirect |
| 21. Q8×Dic151 | C22 | semidirect |
| 23. #18012704 | C22 | semidirect |
| 31. #18012670 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. #18012662 | C22 | semidirect |
| 37. C8×Dic151 | C22 | semidirect |
| 40. #106×C151 | C22 | semidirect |
| 41. #103×C151 | C22 | semidirect |
| 94. C2×Dic151 | SD16 | semidirect |
| 136. C151 | #3101 | semidirect |
| 141. #483 | D151 | semidirect |
| 171. #106 | C2×D151 | semidirect |
| 174. #103 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752764 | 2 |
| C2×#18012701 | 2 |
| #23752542 | 2 |
| #23752501 | 2 |
| #23752416 | 2 |
| #23752365 | 2 |
| #23752362 | 2 |
| #23752299 | 2 |
| #23752297 | 2 |
| #23752262 | 2 |
| #483×C151 | 2 |
| #3101 | 151 |