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. #23756545 | C2 | semidirect |
| 2. #23756544 | C2 | semidirect |
| 3. #23756530 | C2 | semidirect |
| 4. #23756529 | C2 | semidirect |
| 5. #23756526 | C2 | semidirect |
| 6. #23756518 | C2 | semidirect |
| 7. #23756517 | C2 | semidirect |
| 8. C2×#19097551 | C2 | semidirect |
| 9. Q16×D313 | C2 | semidirect |
| 10. #23756505 | C2 | semidirect |
| 11. #137×C313 | C2 | semidirect |
| 87. C313 | #578 | semidirect |
| 94. #137 | D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756545 | 2 |
| #23756544 | 2 |
| #23756530 | 2 |
| #23756529 | 2 |
| #23756526 | 2 |
| #23756518 | 2 |
| #23756517 | 2 |
| C2×#19097551 | 2 |
| Q16×D313 | 2 |
| #23756505 | 2 |
| #137×C313 | 2 |
| #578 | 313 |