Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
160 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 51 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. #24909744 | C2 | semidirect |
| 3. #24905670 | C2 | semidirect |
| 4. #24905660 | C2 | semidirect |
| 7. C83×#1426 | C2 | semidirect |
| 22. Dic664 | Q8 | semidirect |
| 24. D1328 | Q8 | semidirect |
| 81. #1426 | D83 | semidirect |
| 85. C83 | #13710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909744 | 2 |
| #24909343 | 2 |
| #24905670 | 2 |
| #24905660 | 2 |
| #24905651 | 2 |
| #24905649 | 2 |
| C83×#1426 | 2 |
| #13710 | 83 |