Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
198 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 45 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×D4×D313 | C2 | semidirect |
| 2. C2×#19097546 | C2 | semidirect |
| 3. #23756468 | C2 | semidirect |
| 4. #23756419 | C2 | semidirect |
| 5. #23756418 | C2 | semidirect |
| 6. #23756409 | C2 | semidirect |
| 7. C2×D8×C313 | C2 | semidirect |
| 16. C2×#14578809 | C22 | semidirect |
| 17. C4⋊Dic313 | C22 | semidirect |
| 20. C2×D4×C313 | C22 | semidirect |
| 22. C2×C8×C313 | C22 | semidirect |
| 29. D1252 | D4 | semidirect |
| 42. D4×C313 | D4 | semidirect |
| 58. C2×D313 | D8 | semidirect |
| 70. C313 | #447 | semidirect |
| 74. C2×D8 | D313 | semidirect |
| 86. C2×D4 | C2×D313 | semidirect |
| 91. C2×C8 | C2×D313 | semidirect |
| 108. D4 | C22⋊D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D313 | 2 |
| C2×#19097546 | 2 |
| #23756468 | 2 |
| #23756419 | 2 |
| #23756418 | 2 |
| #23756409 | 2 |
| C2×D8×C313 | 2 |
| #447 | 313 |