Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23752767 | C2 | semidirect |
| 3. #23752574 | C2 | semidirect |
| 4. #23752572 | C2 | semidirect |
| 5. #23752571 | C2 | semidirect |
| 6. #23752568 | C2 | semidirect |
| 7. #23752565 | C2 | semidirect |
| 8. #23752219 | C2 | semidirect |
| 10. #23752164 | C2 | semidirect |
| 11. #489×C151 | C2 | semidirect |
| 15. #18012739 | C22 | semidirect |
| 16. #18012730 | C22 | semidirect |
| 30. #18012664 | C22 | semidirect |
| 31. #18012663 | C22 | semidirect |
| 32. #18012662 | C22 | semidirect |
| 36. #18012650 | C22 | semidirect |
| 37. C8×Dic151 | C22 | semidirect |
| 38. C4⋊Q8×C151 | C22 | semidirect |
| 40. #103×C151 | C22 | semidirect |
| 42. #97×C151 | C22 | semidirect |
| 138. C151 | #3140 | semidirect |
| 145. #489 | D151 | semidirect |
| 155. C4⋊Q8 | C2×D151 | semidirect |
| 174. #103 | C2×D151 | semidirect |
| 180. #97 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752767 | 2 |
| #124×D151 | 2 |
| #23752574 | 2 |
| #23752572 | 2 |
| #23752571 | 2 |
| #23752568 | 2 |
| #23752565 | 2 |
| #23752219 | 2 |
| #23752215 | 2 |
| #23752164 | 2 |
| #489×C151 | 2 |
| #3140 | 151 |