Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. #23752769 | C2 | semidirect |
| 3. #23752554 | C2 | semidirect |
| 4. #23752508 | C2 | semidirect |
| 5. #23752503 | C2 | semidirect |
| 6. #23752423 | C2 | semidirect |
| 7. #23752418 | C2 | semidirect |
| 9. #23752320 | C2 | semidirect |
| 10. #23752314 | C2 | semidirect |
| 11. #432×C151 | C2 | semidirect |
| 136. C151 | #3116 | semidirect |
| 148. #432 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752769 | 2 |
| C4×#14559004 | 2 |
| #23752554 | 2 |
| #23752508 | 2 |
| #23752503 | 2 |
| #23752423 | 2 |
| #23752418 | 2 |
| #23752376 | 2 |
| #23752320 | 2 |
| #23752314 | 2 |
| #432×C151 | 2 |
| #3116 | 151 |