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. #23752606 | C2 | semidirect |
| 4. #23752604 | C2 | semidirect |
| 5. #23752582 | C2 | semidirect |
| 6. #23752421 | C2 | semidirect |
| 7. #23752416 | C2 | semidirect |
| 8. #23752369 | C2 | semidirect |
| 10. #23752267 | C2 | semidirect |
| 11. #491×C151 | C2 | semidirect |
| 135. C151 | #3218 | semidirect |
| 142. #491 | 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 |
| #23752747 | 2 |
| #23752606 | 2 |
| #23752604 | 2 |
| #23752582 | 2 |
| #23752421 | 2 |
| #23752416 | 2 |
| #23752369 | 2 |
| #23752352 | 2 |
| #23752267 | 2 |
| #491×C151 | 2 |
| #3218 | 151 |