Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
334 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C2×#18012731 | C2 | semidirect |
| 3. #23752614 | C2 | semidirect |
| 4. #23752567 | C2 | semidirect |
| 5. #23752548 | C2 | semidirect |
| 6. #23752543 | C2 | semidirect |
| 9. #23752520 | C2 | semidirect |
| 10. #23752513 | C2 | semidirect |
| 11. #431×C151 | C2 | semidirect |
| 125. C151 | #3232 | semidirect |
| 137. #431 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752746 | 2 |
| C2×#18012731 | 2 |
| #23752614 | 2 |
| #23752567 | 2 |
| #23752548 | 2 |
| #23752543 | 2 |
| #23752531 | 2 |
| #23752526 | 2 |
| #23752520 | 2 |
| #23752513 | 2 |
| #431×C151 | 2 |
| #3232 | 151 |