Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
366 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23752768 | C2 | semidirect |
| 3. #23752622 | C2 | semidirect |
| 4. #23752621 | C2 | semidirect |
| 5. #23752576 | C2 | semidirect |
| 6. #23752535 | C2 | semidirect |
| 7. #23752534 | C2 | semidirect |
| 8. #23752500 | C2 | semidirect |
| 9. #23752490 | C2 | semidirect |
| 10. #23752267 | C2 | semidirect |
| 11. #490×C151 | C2 | semidirect |
| 128. C151 | #3235 | semidirect |
| 135. #490 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752768 | 2 |
| #23752760 | 2 |
| #23752622 | 2 |
| #23752621 | 2 |
| #23752576 | 2 |
| #23752535 | 2 |
| #23752534 | 2 |
| #23752500 | 2 |
| #23752490 | 2 |
| #23752267 | 2 |
| #490×C151 | 2 |
| #3235 | 151 |