Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
410 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 410 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. #23752618 | C2 | semidirect |
| 3. #23752599 | C2 | semidirect |
| 4. #23752576 | C2 | semidirect |
| 5. #23752574 | C2 | semidirect |
| 6. #23752446 | C2 | semidirect |
| 7. #23752439 | C2 | semidirect |
| 8. #23752322 | C2 | semidirect |
| 9. #23752312 | C2 | semidirect |
| 10. C2×#18012650 | C2 | semidirect |
| 11. #532×C151 | C2 | semidirect |
| 91. C151⋊C8 | #41 | semidirect |
| 137. C151 | #3180 | semidirect |
| 139. #532 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752746 | 2 |
| #23752618 | 2 |
| #23752599 | 2 |
| #23752576 | 2 |
| #23752574 | 2 |
| #23752446 | 2 |
| #23752439 | 2 |
| #23752322 | 2 |
| #23752312 | 2 |
| C2×#18012650 | 2 |
| #532×C151 | 2 |
| #3180 | 151 |