Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 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. Q8×D604 | C2 | semidirect |
| 2. #23752571 | C2 | semidirect |
| 3. #23752562 | C2 | semidirect |
| 4. #23752507 | C2 | semidirect |
| 5. #23752492 | C2 | semidirect |
| 7. #23752414 | C2 | semidirect |
| 8. #23752343 | C2 | semidirect |
| 9. #23752310 | C2 | semidirect |
| 11. #556×C151 | C2 | semidirect |
| 122. C151 | #3367 | semidirect |
| 124. #556 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D604 | 2 |
| #23752571 | 2 |
| #23752562 | 2 |
| #23752507 | 2 |
| #23752492 | 2 |
| #23752424 | 2 |
| #23752414 | 2 |
| #23752343 | 2 |
| #23752310 | 2 |
| C4×#14558989 | 2 |
| #556×C151 | 2 |
| #3367 | 151 |