Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
410 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 103 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. #24906219 | C2 | semidirect |
| 3. #24905507 | C2 | semidirect |
| 4. C83×#2163 | C2 | semidirect |
| 15. #19127452 | C22 | semidirect |
| 17. C4⋊C16×C83 | C22 | semidirect |
| 135. #2163 | D83 | semidirect |
| 138. C83 | #11959 | semidirect |
| 149. C4⋊C16 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128085 | 2 |
| #24906219 | 2 |
| #24905507 | 2 |
| C83×#2163 | 2 |
| #11959 | 83 |