Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1212 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 1212 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. #24915946 | C2 | semidirect |
| 3. #24909112 | C2 | semidirect |
| 4. #24909102 | C2 | semidirect |
| 5. C83×#2884 | C2 | semidirect |
| 6. C22×#13050591 | C4 | semidirect |
| 12. #19128265 | C4 | semidirect |
| 14. #19128208 | C4 | semidirect |
| 16. #19128179 | C4 | semidirect |
| 183. #2884 | D83 | semidirect |
| 186. C83 | #33351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24921118 | 2 |
| #24915946 | 2 |
| #24909112 | 2 |
| #24909102 | 2 |
| C83×#2884 | 2 |
| #33351 | 83 |