Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 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. #23752919 | C2 | semidirect |
| 2. #23752615 | C2 | semidirect |
| 3. #23752553 | C2 | semidirect |
| 4. #23752523 | C2 | semidirect |
| 5. #23752504 | C2 | semidirect |
| 6. #23752502 | C2 | semidirect |
| 7. #23752456 | C2 | semidirect |
| 8. C4×#14558992 | C2 | semidirect |
| 9. #23752290 | C2 | semidirect |
| 10. #23752255 | C2 | semidirect |
| 121. C151 | #3357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752919 | 2 |
| #23752615 | 2 |
| #23752553 | 2 |
| #23752523 | 2 |
| #23752504 | 2 |
| #23752502 | 2 |
| #23752456 | 2 |
| C4×#14558992 | 2 |
| #23752290 | 2 |
| #23752255 | 2 |
| #555×C151 | 2 |
| #3357 | 151 |