Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
512 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. #24918106 | C2 | semidirect |
| 2. #24909623 | C2 | semidirect |
| 3. #24909618 | C2 | semidirect |
| 4. #24909564 | C2 | semidirect |
| 5. #24909549 | C2 | semidirect |
| 6. #24909497 | C2 | semidirect |
| 7. #24909496 | C2 | semidirect |
| 8. #24909221 | C2 | semidirect |
| 9. C83×#2215 | C2 | semidirect |
| 157. #2215 | D83 | semidirect |
| 161. C83 | #33825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918106 | 2 |
| #24909623 | 2 |
| #24909618 | 2 |
| #24909564 | 2 |
| #24909549 | 2 |
| #24909497 | 2 |
| #24909496 | 2 |
| #24909221 | 2 |
| C83×#2215 | 2 |
| #33825 | 83 |