Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23752546 | C2 | semidirect |
| 4. #23752493 | C2 | semidirect |
| 5. #23752492 | C2 | semidirect |
| 6. #23752414 | C2 | semidirect |
| 8. #23752315 | C2 | semidirect |
| 9. #23752313 | C2 | semidirect |
| 10. #23752268 | C2 | semidirect |
| 11. #461×C151 | C2 | semidirect |
| 15. #18012739 | C22 | semidirect |
| 19. Q8×Dic151 | C22 | semidirect |
| 30. #18012673 | C22 | semidirect |
| 31. #18012672 | C22 | semidirect |
| 32. C4⋊(C151⋊C8) | C22 | semidirect |
| 33. #18012663 | C22 | semidirect |
| 37. #18012649 | C22 | semidirect |
| 39. C4⋊Q8×C151 | C22 | semidirect |
| 41. C4⋊C8×C151 | C22 | semidirect |
| 42. #103×C151 | C22 | semidirect |
| 146. C151 | #3110 | semidirect |
| 154. #461 | D151 | semidirect |
| 164. C4⋊Q8 | C2×D151 | semidirect |
| 183. C4⋊C8 | C2×D151 | semidirect |
| 185. #103 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752767 | 2 |
| C4×D4×D151 | 2 |
| #23752546 | 2 |
| #23752493 | 2 |
| #23752492 | 2 |
| #23752414 | 2 |
| #23752361 | 2 |
| #23752315 | 2 |
| #23752313 | 2 |
| #23752268 | 2 |
| #461×C151 | 2 |
| #3110 | 151 |