Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
444 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 444 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. #23752757 | C2 | semidirect |
| 2. C2×#18012726 | C2 | semidirect |
| 3. #23752600 | C2 | semidirect |
| 4. #23752570 | C2 | semidirect |
| 5. #23752426 | C2 | semidirect |
| 6. #23752425 | C2 | semidirect |
| 7. #23752353 | C2 | semidirect |
| 8. #23752350 | C2 | semidirect |
| 9. #23752346 | C2 | semidirect |
| 10. #23752266 | C2 | semidirect |
| 11. #447×C151 | C2 | semidirect |
| 14. C2×#14558993 | C22 | semidirect |
| 15. C2×#14558992 | C22 | semidirect |
| 17. #18012738 | C22 | semidirect |
| 18. #18012735 | C22 | semidirect |
| 26. D4×Dic151 | C22 | semidirect |
| 27. #18012701 | C22 | semidirect |
| 32. Dic151⋊C8 | C22 | semidirect |
| 33. #18012664 | C22 | semidirect |
| 34. #18012662 | C22 | semidirect |
| 37. #18012649 | C22 | semidirect |
| 152. C151 | #3213 | semidirect |
| 163. #447 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752757 | 2 |
| C2×#18012726 | 2 |
| #23752600 | 2 |
| #23752570 | 2 |
| #23752426 | 2 |
| #23752425 | 2 |
| #23752353 | 2 |
| #23752350 | 2 |
| #23752346 | 2 |
| #23752266 | 2 |
| #447×C151 | 2 |
| #3213 | 151 |