Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
658 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 658 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. #24912417 | C2 | semidirect |
| 3. #24906144 | C2 | semidirect |
| 4. #24905958 | C2 | semidirect |
| 5. #24905853 | C2 | semidirect |
| 6. #24905365 | C2 | semidirect |
| 7. C83×#3206 | C2 | semidirect |
| 84. C2×D332 | SD16 | semidirect |
| 217. #3206 | D83 | semidirect |
| 224. C83 | #10240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916923 | 2 |
| #24912417 | 2 |
| #24906144 | 2 |
| #24905958 | 2 |
| #24905853 | 2 |
| #24905365 | 2 |
| C83×#3206 | 2 |
| #10240 | 83 |