Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×Q8×D313 | C2 | semidirect |
| 3. #23756496 | C2 | semidirect |
| 4. #23756483 | C2 | semidirect |
| 5. #23756482 | C2 | semidirect |
| 6. #23756479 | C2 | semidirect |
| 7. #23756477 | C2 | semidirect |
| 8. #23756476 | C2 | semidirect |
| 9. #23756473 | C2 | semidirect |
| 10. #23756455 | C2 | semidirect |
| 11. C22⋊Q8×C313 | C2 | semidirect |
| 83. C313 | #536 | semidirect |
| 94. C22⋊Q8 | D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097561 | 2 |
| C2×Q8×D313 | 2 |
| #23756496 | 2 |
| #23756483 | 2 |
| #23756482 | 2 |
| #23756479 | 2 |
| #23756477 | 2 |
| #23756476 | 2 |
| #23756473 | 2 |
| #23756455 | 2 |
| C22⋊Q8×C313 | 2 |
| #536 | 313 |