Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23752763 | C2 | semidirect |
| 2. #23752741 | C2 | semidirect |
| 3. #23752618 | C2 | semidirect |
| 4. #23752602 | C2 | semidirect |
| 5. #23752577 | C2 | semidirect |
| 6. #23752464 | C2 | semidirect |
| 7. #23752461 | C2 | semidirect |
| 8. #23752297 | C2 | semidirect |
| 9. #23752292 | C2 | semidirect |
| 10. #23752164 | C2 | semidirect |
| 11. #489×C151 | C2 | semidirect |
| 100. C151⋊C8 | #41 | semidirect |
| 137. C151 | #3171 | semidirect |
| 144. #489 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752763 | 2 |
| #23752741 | 2 |
| #23752618 | 2 |
| #23752602 | 2 |
| #23752577 | 2 |
| #23752464 | 2 |
| #23752461 | 2 |
| #23752297 | 2 |
| #23752292 | 2 |
| #23752164 | 2 |
| #489×C151 | 2 |
| #3171 | 151 |