Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
498 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #24908404 | C2 | semidirect |
| 4. #24905866 | C2 | semidirect |
| 6. #24905293 | C2 | semidirect |
| 7. C83×#3104 | C2 | semidirect |
| 194. #3104 | D83 | semidirect |
| 200. C83 | #10035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917811 | 2 |
| #24917494 | 2 |
| #24908404 | 2 |
| #24905866 | 2 |
| #24905863 | 2 |
| #24905293 | 2 |
| C83×#3104 | 2 |
| #10035 | 83 |