Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23752922 | C2 | semidirect |
| 2. #23752566 | C2 | semidirect |
| 3. #23752558 | C2 | semidirect |
| 4. #23752512 | C2 | semidirect |
| 5. #23752507 | C2 | semidirect |
| 6. #23752424 | C2 | semidirect |
| 8. Q8×C151⋊C8 | C2 | semidirect |
| 9. C4×#14558991 | C2 | semidirect |
| 10. C4×#14558989 | C2 | semidirect |
| 11. #559×C151 | C2 | semidirect |
| 122. C151 | #3361 | semidirect |
| 124. #559 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752922 | 2 |
| #23752566 | 2 |
| #23752558 | 2 |
| #23752512 | 2 |
| #23752507 | 2 |
| #23752424 | 2 |
| #23752404 | 2 |
| Q8×C151⋊C8 | 2 |
| C4×#14558991 | 2 |
| C4×#14558989 | 2 |
| #559×C151 | 2 |
| #3361 | 151 |