Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
474 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 474 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. #24916478 | C2 | semidirect |
| 3. #24906060 | C2 | semidirect |
| 4. #24905898 | C2 | semidirect |
| 5. #24905814 | C2 | semidirect |
| 6. #24905374 | C2 | semidirect |
| 7. C83×#1299 | C2 | semidirect |
| 214. #1299 | D83 | semidirect |
| 215. C83 | #9349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916958 | 2 |
| #24916478 | 2 |
| #24906060 | 2 |
| #24905898 | 2 |
| #24905814 | 2 |
| #24905374 | 2 |
| C83×#1299 | 2 |
| #9349 | 83 |