Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
662 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 662 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. #24910637 | C2 | semidirect |
| 3. #24908287 | C2 | semidirect |
| 4. #24905345 | C2 | semidirect |
| 5. C2×#329×C83 | C2 | semidirect |
| 10. #19128091 | C4 | semidirect |
| 34. #14581789 | C2×C4 | semidirect |
| 44. #14581703 | C2×C4 | semidirect |
| 182. C2×#329 | D83 | semidirect |
| 184. C83 | #9001 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128091 | 2 |
| #24910637 | 2 |
| #24908287 | 2 |
| #24905345 | 2 |
| C2×#329×C83 | 2 |
| #9001 | 83 |