Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
428 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 2. C4×Q8×D151 | C2 | semidirect |
| 3. #23752532 | C2 | semidirect |
| 4. #23752494 | C2 | semidirect |
| 5. #23752413 | C2 | semidirect |
| 6. #23752412 | C2 | semidirect |
| 7. #23752352 | C2 | semidirect |
| 8. #23752299 | C2 | semidirect |
| 9. #23752297 | C2 | semidirect |
| 10. #23752264 | C2 | semidirect |
| 11. #475×C151 | C2 | semidirect |
| 87. Dic302 | #41 | semidirect |
| 104. C4×D151 | SD16 | semidirect |
| 108. Q8×C151 | #41 | semidirect |
| 140. C151 | #3103 | semidirect |
| 146. #475 | D151 | semidirect |
| 231. Q8 | #14559005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23752763 | 2 |
| C4×Q8×D151 | 2 |
| #23752532 | 2 |
| #23752494 | 2 |
| #23752413 | 2 |
| #23752412 | 2 |
| #23752352 | 2 |
| #23752299 | 2 |
| #23752297 | 2 |
| #23752264 | 2 |
| #475×C151 | 2 |
| #3103 | 151 |