Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
798 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 179 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. #24918021 | C2 | semidirect |
| 2. #24918020 | C2 | semidirect |
| 3. #24917972 | C2 | semidirect |
| 5. #24907097 | C2 | semidirect |
| 6. #24907096 | C2 | semidirect |
| 7. #24907089 | C2 | semidirect |
| 8. #24907084 | C2 | semidirect |
| 9. #24907083 | C2 | semidirect |
| 10. #322×D83 | C2 | semidirect |
| 11. C83×#1715 | C2 | semidirect |
| 106. C8×D83 | SD16 | semidirect |
| 188. #1715 | D83 | semidirect |
| 192. C83 | #19608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918021 | 2 |
| #24918020 | 2 |
| #24917972 | 2 |
| #24917890 | 2 |
| #24907097 | 2 |
| #24907096 | 2 |
| #24907089 | 2 |
| #24907084 | 2 |
| #24907083 | 2 |
| #322×D83 | 2 |
| C83×#1715 | 2 |
| #19608 | 83 |