Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
190 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 50 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. #23756559 | C2 | semidirect |
| 7. #19097569 | C22 | semidirect |
| 8. C4⋊#11929411 | C22 | semidirect |
| 12. C2×D1252 | C4 | semidirect |
| 16. D4×D313 | C4 | semidirect |
| 19. C2×D4×C313 | C4 | semidirect |
| 61. C313 | #418 | semidirect |
| 74. C2×D4 | #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 |
| #23756559 | 2 |
| C2×D4×D313 | 2 |
| #418 | 313 |