Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23756544 | C2 | semidirect |
| 2. #23756527 | C2 | semidirect |
| 3. #23756526 | C2 | semidirect |
| 4. #23756516 | C2 | semidirect |
| 5. C2×Dic1252 | C2 | semidirect |
| 6. Q16×D313 | C2 | semidirect |
| 7. #23756503 | C2 | semidirect |
| 8. #135×C313 | C2 | semidirect |
| 59. C313 | #578 | semidirect |
| 65. #135 | D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756544 | 2 |
| #23756527 | 2 |
| #23756526 | 2 |
| #23756516 | 2 |
| C2×Dic1252 | 2 |
| Q16×D313 | 2 |
| #23756503 | 2 |
| #135×C313 | 2 |
| #578 | 313 |