Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
438 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23752762 | C2 | semidirect |
| 2. #23752588 | C2 | semidirect |
| 3. #23752586 | C2 | semidirect |
| 4. #23752562 | C2 | semidirect |
| 5. #23752558 | C2 | semidirect |
| 6. #23752424 | C2 | semidirect |
| 7. #23752357 | C2 | semidirect |
| 8. #23752265 | C2 | semidirect |
| 9. #532×C151 | C2 | semidirect |
| 120. C151 | #3207 | semidirect |
| 123. #532 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752762 | 2 |
| #23752588 | 2 |
| #23752586 | 2 |
| #23752562 | 2 |
| #23752558 | 2 |
| #23752424 | 2 |
| #23752357 | 2 |
| #23752265 | 2 |
| #532×C151 | 2 |
| #3207 | 151 |