Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#18012762 | C2 | semidirect |
| 2. C2×#18012760 | C2 | semidirect |
| 3. #23752763 | C2 | semidirect |
| 4. #23752761 | C2 | semidirect |
| 5. #23752605 | C2 | semidirect |
| 6. #23752604 | C2 | semidirect |
| 7. #23752602 | C2 | semidirect |
| 8. #23752601 | C2 | semidirect |
| 9. #23752598 | C2 | semidirect |
| 10. #97×D151 | C2 | semidirect |
| 11. #497×C151 | C2 | semidirect |
| 65. C8×D151 | D4 | semidirect |
| 133. C151 | #3150 | semidirect |
| 141. #497 | D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012762 | 2 |
| C2×#18012760 | 2 |
| #23752763 | 2 |
| #23752761 | 2 |
| #23752605 | 2 |
| #23752604 | 2 |
| #23752602 | 2 |
| #23752601 | 2 |
| #23752598 | 2 |
| #97×D151 | 2 |
| #497×C151 | 2 |
| #3150 | 151 |