Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 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. #23752764 | C2 | semidirect |
| 3. #23752605 | C2 | semidirect |
| 4. #23752573 | C2 | semidirect |
| 5. #23752437 | C2 | semidirect |
| 6. #23752436 | C2 | semidirect |
| 7. #23752368 | C2 | semidirect |
| 10. #23752266 | C2 | semidirect |
| 11. #451×C151 | C2 | semidirect |
| 13. C2×#14558994 | C22 | semidirect |
| 16. #18012738 | C22 | semidirect |
| 17. #18012737 | C22 | semidirect |
| 25. Q8×Dic151 | C22 | semidirect |
| 27. #18012704 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. #18012663 | C22 | semidirect |
| 37. #18012649 | C22 | semidirect |
| 39. C2×Q16×C151 | C22 | semidirect |
| 41. #103×C151 | C22 | semidirect |
| 139. C151 | #3215 | semidirect |
| 148. #451 | D151 | semidirect |
| 155. C2×Q16 | C2×D151 | semidirect |
| 177. #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×#18012728 | 2 |
| #23752605 | 2 |
| #23752573 | 2 |
| #23752437 | 2 |
| #23752436 | 2 |
| #23752368 | 2 |
| #23752365 | 2 |
| #23752362 | 2 |
| #23752266 | 2 |
| #451×C151 | 2 |
| #3215 | 151 |