Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
574 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24918388 | C2 | semidirect |
| 3. #24908453 | C2 | semidirect |
| 4. #24906054 | C2 | semidirect |
| 5. #24905880 | C2 | semidirect |
| 6. #24905353 | C2 | semidirect |
| 7. C83×#3152 | C2 | semidirect |
| 191. #3152 | D83 | semidirect |
| 196. C83 | #10106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918841 | 2 |
| #24918388 | 2 |
| #24908453 | 2 |
| #24906054 | 2 |
| #24905880 | 2 |
| #24905353 | 2 |
| C83×#3152 | 2 |
| #10106 | 83 |