Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
412 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 93 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×#19127513 | C2 | semidirect |
| 4. C2×#19127501 | C2 | semidirect |
| 5. #24909077 | C2 | semidirect |
| 6. #24905571 | C2 | semidirect |
| 7. C83×#1816 | C2 | semidirect |
| 176. #1816 | D83 | semidirect |
| 178. C83 | #13393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127971 | 2 |
| C2×#19127530 | 2 |
| C2×#19127513 | 2 |
| C2×#19127501 | 2 |
| #24909077 | 2 |
| #24905571 | 2 |
| C83×#1816 | 2 |
| #13393 | 83 |