Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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. C4⋊Q8×D151 | C2 | semidirect |
| 3. #23752607 | C2 | semidirect |
| 4. #23752581 | C2 | semidirect |
| 5. #23752580 | C2 | semidirect |
| 6. #23752420 | C2 | semidirect |
| 7. #23752415 | C2 | semidirect |
| 8. #23752366 | C2 | semidirect |
| 10. #23752267 | C2 | semidirect |
| 11. #497×C151 | C2 | semidirect |
| 135. C151 | #3218 | semidirect |
| 140. #497 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D151 | 2 |
| #23752741 | 2 |
| #23752607 | 2 |
| #23752581 | 2 |
| #23752580 | 2 |
| #23752420 | 2 |
| #23752415 | 2 |
| #23752366 | 2 |
| #23752349 | 2 |
| #23752267 | 2 |
| #497×C151 | 2 |
| #3218 | 151 |