Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
388 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23752817 | C2 | semidirect |
| 2. #23752788 | C2 | semidirect |
| 3. #23752601 | C2 | semidirect |
| 4. #23752585 | C2 | semidirect |
| 5. #23752581 | C2 | semidirect |
| 6. #23752567 | C2 | semidirect |
| 7. #23752428 | C2 | semidirect |
| 8. #23752418 | C2 | semidirect |
| 9. #23752359 | C2 | semidirect |
| 10. #23752353 | C2 | semidirect |
| 11. #433×C151 | C2 | semidirect |
| 120. C151 | #3221 | semidirect |
| 132. #433 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752817 | 2 |
| #23752788 | 2 |
| #23752601 | 2 |
| #23752585 | 2 |
| #23752581 | 2 |
| #23752567 | 2 |
| #23752428 | 2 |
| #23752418 | 2 |
| #23752359 | 2 |
| #23752353 | 2 |
| #433×C151 | 2 |
| #3221 | 151 |