Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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. #23756585 | C2 | semidirect |
| 2. #23756584 | C2 | semidirect |
| 3. #23756568 | C2 | semidirect |
| 4. #23756562 | C2 | semidirect |
| 5. #23756561 | C2 | semidirect |
| 6. #23756551 | C2 | semidirect |
| 18. #19097551 | C4 | semidirect |
| 19. #19097550 | C4 | semidirect |
| 20. #19097546 | C4 | semidirect |
| 22. SD16×C313 | C4 | semidirect |
| 51. C313 | #444 | semidirect |
| 64. SD16 | #11929411 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756585 | 2 |
| #23756584 | 2 |
| #23756568 | 2 |
| #23756562 | 2 |
| #23756561 | 2 |
| #23756551 | 2 |
| #23756518 | 2 |
| #444 | 313 |