Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23752762 | C2 | semidirect |
| 2. C4×#14559004 | C2 | semidirect |
| 3. #23752537 | C2 | semidirect |
| 4. #23752498 | C2 | semidirect |
| 5. #23752493 | C2 | semidirect |
| 6. #23752413 | C2 | semidirect |
| 7. #23752408 | C2 | semidirect |
| 8. #23752359 | C2 | semidirect |
| 9. #23752325 | C2 | semidirect |
| 10. #23752314 | C2 | semidirect |
| 11. #432×C151 | C2 | semidirect |
| 87. Dic302 | #41 | semidirect |
| 93. D604 | #41 | semidirect |
| 144. C151 | #3115 | semidirect |
| 156. #432 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752762 | 2 |
| C4×#14559004 | 2 |
| #23752537 | 2 |
| #23752498 | 2 |
| #23752493 | 2 |
| #23752413 | 2 |
| #23752408 | 2 |
| #23752359 | 2 |
| #23752325 | 2 |
| #23752314 | 2 |
| #432×C151 | 2 |
| #3115 | 151 |