Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#18012787 | C2 | semidirect |
| 2. C2×#18012759 | C2 | semidirect |
| 3. #23752790 | C2 | semidirect |
| 4. #23752373 | C2 | semidirect |
| 5. #23752366 | C2 | semidirect |
| 6. #23752356 | C2 | semidirect |
| 7. #23752349 | C2 | semidirect |
| 8. #23752214 | C2 | semidirect |
| 9. C2×#18012663 | C2 | semidirect |
| 10. #23752180 | C2 | semidirect |
| 11. C2×#137×C151 | C2 | semidirect |
| 52. #14559004 | D4 | semidirect |
| 86. C2×Q8×C151 | D4 | semidirect |
| 169. C151 | #3013 | semidirect |
| 172. C2×#137 | D151 | semidirect |
| 233. C2×Q8 | C22⋊D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012787 | 2 |
| C2×#18012759 | 2 |
| #23752790 | 2 |
| #23752373 | 2 |
| #23752366 | 2 |
| #23752356 | 2 |
| #23752349 | 2 |
| #23752214 | 2 |
| C2×#18012663 | 2 |
| #23752180 | 2 |
| C2×#137×C151 | 2 |
| #3013 | 151 |