Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
224 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 3. #24906269 | C2 | semidirect |
| 4. #24905426 | C2 | semidirect |
| 6. #24905382 | C2 | semidirect |
| 7. C83×#1371 | C2 | semidirect |
| 48. Dic332 | M16 | semidirect |
| 109. #1371 | D83 | semidirect |
| 113. C83 | #12075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14581737 | 2 |
| #24906347 | 2 |
| #24906269 | 2 |
| #24905426 | 2 |
| #24905423 | 2 |
| #24905382 | 2 |
| C83×#1371 | 2 |
| #12075 | 83 |