Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
458 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 458 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. C2×#19127523 | C2 | semidirect |
| 3. C2×#19127515 | C2 | semidirect |
| 4. C2×#19127513 | C2 | semidirect |
| 5. C2×#19127482 | C2 | semidirect |
| 6. #24907502 | C2 | semidirect |
| 7. C83×#1383 | C2 | semidirect |
| 46. #14581732 | D4 | semidirect |
| 178. #1383 | D83 | semidirect |
| 179. C83 | #13398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127955 | 2 |
| C2×#19127523 | 2 |
| C2×#19127515 | 2 |
| C2×#19127513 | 2 |
| C2×#19127482 | 2 |
| #24907502 | 2 |
| C83×#1383 | 2 |
| #13398 | 83 |