Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
852 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 87 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. #24918270 | C2 | semidirect |
| 2. C2×#19127852 | C2 | semidirect |
| 4. #24905828 | C2 | semidirect |
| 5. #24905824 | C2 | semidirect |
| 6. #24905350 | C2 | semidirect |
| 7. C83×#1783 | C2 | semidirect |
| 235. #1783 | D83 | semidirect |
| 239. C83 | #9987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918270 | 2 |
| C2×#19127852 | 2 |
| C2×#19127835 | 2 |
| #24905828 | 2 |
| #24905824 | 2 |
| #24905350 | 2 |
| C83×#1783 | 2 |
| #9987 | 83 |