Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 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. #23752746 | C2 | semidirect |
| 2. #23752614 | C2 | semidirect |
| 3. #23752596 | C2 | semidirect |
| 4. #23752567 | C2 | semidirect |
| 5. #23752470 | C2 | semidirect |
| 7. #23752458 | C2 | semidirect |
| 8. #23752325 | C2 | semidirect |
| 9. #23752320 | C2 | semidirect |
| 10. #23752314 | C2 | semidirect |
| 11. C4×M16×C151 | C2 | semidirect |
| 109. C151 | #3183 | semidirect |
| 121. C4×M16 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752746 | 2 |
| #23752614 | 2 |
| #23752596 | 2 |
| #23752567 | 2 |
| #23752470 | 2 |
| #23752465 | 2 |
| #23752458 | 2 |
| #23752325 | 2 |
| #23752320 | 2 |
| #23752314 | 2 |
| C4×M16×C151 | 2 |
| #3183 | 151 |