Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 394 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. #23752769 | C2 | semidirect |
| 3. #23752592 | C2 | semidirect |
| 4. #23752585 | C2 | semidirect |
| 5. #23752563 | C2 | semidirect |
| 6. #23752559 | C2 | semidirect |
| 7. #23752435 | C2 | semidirect |
| 8. #23752376 | C2 | semidirect |
| 9. #431×C151 | C2 | semidirect |
| 112. C151 | #3210 | semidirect |
| 122. #431 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752769 | 2 |
| #23752762 | 2 |
| #23752592 | 2 |
| #23752585 | 2 |
| #23752563 | 2 |
| #23752559 | 2 |
| #23752435 | 2 |
| #23752376 | 2 |
| #431×C151 | 2 |
| #3210 | 151 |