Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
154 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 48 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. D313⋊M16 | C2 | semidirect |
| 2. #23756576 | C2 | semidirect |
| 3. #23756562 | C2 | semidirect |
| 5. #19097571 | C22 | semidirect |
| 10. C4×#11929411 | C22 | semidirect |
| 13. #19097562 | C4 | semidirect |
| 16. C2×D1252 | C4 | semidirect |
| 19. C2×Q8×C313 | C4 | semidirect |
| 56. C313 | #421 | semidirect |
| 66. C2×Q8 | #11929411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D313⋊M16 | 2 |
| #23756576 | 2 |
| #23756562 | 2 |
| C2×#19097562 | 2 |
| #421 | 313 |