Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
386 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 91 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. #24906121 | C2 | semidirect |
| 4. #24905961 | C2 | semidirect |
| 6. #24905294 | C2 | semidirect |
| 7. C83×#1940 | C2 | semidirect |
| 190. #1940 | D83 | semidirect |
| 196. C83 | #10547 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917809 | 2 |
| #24906121 | 2 |
| #24906113 | 2 |
| #24905961 | 2 |
| #24905957 | 2 |
| #24905294 | 2 |
| C83×#1940 | 2 |
| #10547 | 83 |