Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 2. #23756530 | C2 | semidirect |
| 3. #23756527 | C2 | semidirect |
| 4. #23756485 | C2 | semidirect |
| 5. #23756425 | C2 | semidirect |
| 6. #23756413 | C2 | semidirect |
| 7. #104×C313 | C2 | semidirect |
| 11. C2×Dic626 | C22 | semidirect |
| 20. #19097545 | C22 | semidirect |
| 23. M16×C313 | C22 | semidirect |
| 24. C42×C313 | C22 | semidirect |
| 64. C313 | #455 | semidirect |
| 71. #104 | D313 | semidirect |
| 87. M16 | C2×D313 | semidirect |
| 89. C42 | C2×D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756543 | 2 |
| #23756530 | 2 |
| #23756527 | 2 |
| #23756485 | 2 |
| #23756425 | 2 |
| #23756413 | 2 |
| #104×C313 | 2 |
| #455 | 313 |