Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
454 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 81 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. #24918015 | C2 | semidirect |
| 4. #24905935 | C2 | semidirect |
| 6. #24905820 | C2 | semidirect |
| 7. C83×#1291 | C2 | semidirect |
| 188. #1291 | D83 | semidirect |
| 189. C83 | #10126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918655 | 2 |
| #24918476 | 2 |
| #24918015 | 2 |
| #24905935 | 2 |
| #24905881 | 2 |
| #24905820 | 2 |
| C83×#1291 | 2 |
| #10126 | 83 |