Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23752760 | C2 | semidirect |
| 2. #23752759 | C2 | semidirect |
| 3. #23752503 | C2 | semidirect |
| 4. #23752502 | C2 | semidirect |
| 5. #23752500 | C2 | semidirect |
| 6. #23752464 | C2 | semidirect |
| 7. #23752462 | C2 | semidirect |
| 8. #23752405 | C2 | semidirect |
| 9. #23752404 | C2 | semidirect |
| 10. #23752234 | C2 | semidirect |
| 11. #459×C151 | C2 | semidirect |
| 150. C151 | #3253 | semidirect |
| 161. #459 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752760 | 2 |
| #23752759 | 2 |
| #23752503 | 2 |
| #23752502 | 2 |
| #23752500 | 2 |
| #23752464 | 2 |
| #23752462 | 2 |
| #23752405 | 2 |
| #23752404 | 2 |
| #23752234 | 2 |
| #459×C151 | 2 |
| #3253 | 151 |