Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
442 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 113 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×#19127530 | C2 | semidirect |
| 3. C2×#19127514 | C2 | semidirect |
| 4. C2×#19127513 | C2 | semidirect |
| 5. #24909060 | C2 | semidirect |
| 6. #24908373 | C2 | semidirect |
| 7. C83×#1978 | C2 | semidirect |
| 12. C2×#14581733 | C4 | semidirect |
| 171. #1978 | D83 | semidirect |
| 172. C83 | #13245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581733 | 2 |
| C2×#19127530 | 2 |
| C2×#19127514 | 2 |
| C2×#19127513 | 2 |
| #24909060 | 2 |
| #24908373 | 2 |
| C83×#1978 | 2 |
| #13245 | 83 |