Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
474 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 474 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. #24906226 | C2 | semidirect |
| 3. #24906060 | C2 | semidirect |
| 4. #24905814 | C2 | semidirect |
| 5. C83×#1451 | C2 | semidirect |
| 150. #1451 | D83 | semidirect |
| 151. C83 | #9791 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128085 | 2 |
| #24906226 | 2 |
| #24906060 | 2 |
| #24905814 | 2 |
| C83×#1451 | 2 |
| #9791 | 83 |