Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 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. #23752932 | C2 | semidirect |
| 2. #23752558 | C2 | semidirect |
| 3. #23752533 | C2 | semidirect |
| 4. #23752497 | C2 | semidirect |
| 5. #23752439 | C2 | semidirect |
| 6. #23752409 | C2 | semidirect |
| 7. #23752374 | C2 | semidirect |
| 8. C4×#14558994 | C2 | semidirect |
| 9. D4×C151⋊C8 | C2 | semidirect |
| 10. #23752208 | C2 | semidirect |
| 127. C151 | #3304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752932 | 2 |
| #23752558 | 2 |
| #23752533 | 2 |
| #23752497 | 2 |
| #23752439 | 2 |
| #23752409 | 2 |
| #23752374 | 2 |
| C4×#14558994 | 2 |
| D4×C151⋊C8 | 2 |
| #23752208 | 2 |
| #550×C151 | 2 |
| #3304 | 151 |