Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23752768 | C2 | semidirect |
| 3. #23752580 | C2 | semidirect |
| 4. #23752578 | C2 | semidirect |
| 5. #23752577 | C2 | semidirect |
| 6. #23752573 | C2 | semidirect |
| 7. #23752207 | C2 | semidirect |
| 8. #97×D151 | C2 | semidirect |
| 9. #491×C151 | C2 | semidirect |
| 90. C151 | #3135 | semidirect |
| 95. #491 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752768 | 2 |
| #23752763 | 2 |
| #23752580 | 2 |
| #23752578 | 2 |
| #23752577 | 2 |
| #23752573 | 2 |
| #23752207 | 2 |
| #97×D151 | 2 |
| #491×C151 | 2 |
| #3135 | 151 |