Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
330 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 87 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. #24909720 | C2 | semidirect |
| 2. #24909718 | C2 | semidirect |
| 3. #24909715 | C2 | semidirect |
| 5. #24907069 | C2 | semidirect |
| 6. C8×C83⋊C16 | C2 | semidirect |
| 7. C83×#1709 | C2 | semidirect |
| 104. #1709 | D83 | semidirect |
| 106. C83 | #12518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909720 | 2 |
| #24909718 | 2 |
| #24909715 | 2 |
| #24909712 | 2 |
| #24907069 | 2 |
| C8×C83⋊C16 | 2 |
| C83×#1709 | 2 |
| #12518 | 83 |