Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 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 |
|---|---|---|
| 1. #23752768 | C2 | semidirect |
| 3. #23752569 | C2 | semidirect |
| 4. #23752567 | C2 | semidirect |
| 5. #23752566 | C2 | semidirect |
| 6. #23752561 | C2 | semidirect |
| 7. #23752557 | C2 | semidirect |
| 8. #23752207 | C2 | semidirect |
| 9. #23752205 | C2 | semidirect |
| 10. C4×C8×D151 | C2 | semidirect |
| 11. #488×C151 | C2 | semidirect |
| 114. C151 | #3131 | semidirect |
| 121. #488 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752768 | 2 |
| #23752761 | 2 |
| #23752569 | 2 |
| #23752567 | 2 |
| #23752566 | 2 |
| #23752561 | 2 |
| #23752557 | 2 |
| #23752207 | 2 |
| #23752205 | 2 |
| C4×C8×D151 | 2 |
| #488×C151 | 2 |
| #3131 | 151 |