Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23752604 | C2 | semidirect |
| 3. #23752574 | C2 | semidirect |
| 4. #23752422 | C2 | semidirect |
| 5. #23752412 | C2 | semidirect |
| 6. #23752372 | C2 | semidirect |
| 7. #23752269 | C2 | semidirect |
| 8. #533×C151 | C2 | semidirect |
| 109. C151 | #3216 | semidirect |
| 111. #533 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752762 | 2 |
| #23752604 | 2 |
| #23752574 | 2 |
| #23752422 | 2 |
| #23752412 | 2 |
| #23752372 | 2 |
| #23752269 | 2 |
| #533×C151 | 2 |
| #3216 | 151 |