Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
434 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 434 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. #23752760 | C2 | semidirect |
| 2. #23752759 | C2 | semidirect |
| 3. #23752600 | C2 | semidirect |
| 4. #23752570 | C2 | semidirect |
| 5. #23752418 | C2 | semidirect |
| 6. #23752417 | C2 | semidirect |
| 7. #23752404 | C2 | semidirect |
| 8. #23752358 | C2 | semidirect |
| 9. #23752354 | C2 | semidirect |
| 10. #23752268 | C2 | semidirect |
| 11. #459×C151 | C2 | semidirect |
| 153. C151 | #3214 | semidirect |
| 162. #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 |
| #23752600 | 2 |
| #23752570 | 2 |
| #23752418 | 2 |
| #23752417 | 2 |
| #23752404 | 2 |
| #23752358 | 2 |
| #23752354 | 2 |
| #23752268 | 2 |
| #459×C151 | 2 |
| #3214 | 151 |