Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 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. Q8×D604 | C2 | semidirect |
| 3. #23752564 | C2 | semidirect |
| 4. #23752544 | C2 | semidirect |
| 5. #23752442 | C2 | semidirect |
| 6. #23752418 | C2 | semidirect |
| 7. #23752352 | C2 | semidirect |
| 8. C4×#14558991 | C2 | semidirect |
| 9. #23752277 | C2 | semidirect |
| 10. #103×D151 | C2 | semidirect |
| 11. #475×C151 | C2 | semidirect |
| 85. D604 | SD16 | semidirect |
| 98. Q8×C151 | #41 | semidirect |
| 128. C151 | #3298 | semidirect |
| 134. #475 | D151 | semidirect |
| 213. Q8 | #14559005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D604 | 2 |
| #23752865 | 2 |
| #23752564 | 2 |
| #23752544 | 2 |
| #23752442 | 2 |
| #23752418 | 2 |
| #23752352 | 2 |
| C4×#14558991 | 2 |
| #23752277 | 2 |
| #103×D151 | 2 |
| #475×C151 | 2 |
| #3298 | 151 |