Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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×#19127513 | C2 | semidirect |
| 3. C2×#19127510 | C2 | semidirect |
| 4. C2×#19127478 | C2 | semidirect |
| 5. #24908354 | C2 | semidirect |
| 6. #24908337 | C2 | semidirect |
| 7. C2×#365×C83 | C2 | semidirect |
| 12. C2×#14581737 | C4 | semidirect |
| 13. C2×D1328 | C4 | semidirect |
| 111. C16×C83 | C22⋊C4 | semidirect |
| 174. C2×#365 | D83 | semidirect |
| 180. C83 | #13249 | semidirect |
| 284. C16 | (C2×D83)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128139 | 2 |
| C2×#19127513 | 2 |
| C2×#19127510 | 2 |
| C2×#19127478 | 2 |
| #24908354 | 2 |
| #24908337 | 2 |
| C2×#365×C83 | 2 |
| #13249 | 83 |