Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 386 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. #23752818 | C2 | semidirect |
| 2. #23752816 | C2 | semidirect |
| 3. #23752611 | C2 | semidirect |
| 4. #23752588 | C2 | semidirect |
| 5. #23752577 | C2 | semidirect |
| 6. #23752464 | C2 | semidirect |
| 7. #23752447 | C2 | semidirect |
| 8. #23752321 | C2 | semidirect |
| 9. #23752292 | C2 | semidirect |
| 10. #23752169 | C2 | semidirect |
| 11. #490×C151 | C2 | semidirect |
| 114. C151 | #3176 | semidirect |
| 121. #490 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752818 | 2 |
| #23752816 | 2 |
| #23752611 | 2 |
| #23752588 | 2 |
| #23752577 | 2 |
| #23752464 | 2 |
| #23752447 | 2 |
| #23752321 | 2 |
| #23752292 | 2 |
| #23752169 | 2 |
| #490×C151 | 2 |
| #3176 | 151 |