Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1188 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1188 conjugacy classes of subgroups — too many to draw. Only its 271 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. #24915927 | C2 | semidirect |
| 3. #24909137 | C2 | semidirect |
| 4. #24909126 | C2 | semidirect |
| 5. C83×#2884 | C2 | semidirect |
| 6. C2×#14581839 | C4 | semidirect |
| 11. #19128275 | C4 | semidirect |
| 14. C2×#14581790 | C4 | semidirect |
| 16. #41×Dic83 | C4 | semidirect |
| 182. #2884 | D83 | semidirect |
| 185. C83 | #33360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24921244 | 2 |
| #24915927 | 2 |
| #24909137 | 2 |
| #24909126 | 2 |
| C83×#2884 | 2 |
| #33360 | 83 |