Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #23752941 | C2 | semidirect |
| 3. #23752568 | C2 | semidirect |
| 5. #23752515 | C2 | semidirect |
| 6. #23752497 | C2 | semidirect |
| 7. #23752436 | C2 | semidirect |
| 9. C8×Dic302 | C2 | semidirect |
| 10. #23752297 | C2 | semidirect |
| 11. C4×Q16×C151 | C2 | semidirect |
| 117. C151 | #3365 | semidirect |
| 128. C4×Q16 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752947 | 2 |
| #23752941 | 2 |
| #23752568 | 2 |
| #23752559 | 2 |
| #23752515 | 2 |
| #23752497 | 2 |
| #23752436 | 2 |
| #23752412 | 2 |
| C8×Dic302 | 2 |
| #23752297 | 2 |
| C4×Q16×C151 | 2 |
| #3365 | 151 |