Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 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. #24909237 | C2 | semidirect |
| 3. C2×#19127513 | C2 | semidirect |
| 4. #24909178 | C2 | semidirect |
| 5. #24909091 | C2 | semidirect |
| 6. #24905564 | C2 | semidirect |
| 7. C83×#1814 | C2 | semidirect |
| 42. C2×C83⋊C16 | D4 | semidirect |
| 171. #1814 | D83 | semidirect |
| 173. C83 | #13396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917111 | 2 |
| #24909237 | 2 |
| C2×#19127513 | 2 |
| #24909178 | 2 |
| #24909091 | 2 |
| #24905564 | 2 |
| C83×#1814 | 2 |
| #13396 | 83 |