Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
306 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 57 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. #24909663 | C2 | semidirect |
| 3. #24909661 | C2 | semidirect |
| 5. #24905480 | C2 | semidirect |
| 7. C83×#1350 | C2 | semidirect |
| 156. #1350 | D83 | semidirect |
| 158. C83 | #12286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918353 | 2 |
| #24909663 | 2 |
| #24909661 | 2 |
| #24908905 | 2 |
| #24905480 | 2 |
| #24905388 | 2 |
| C83×#1350 | 2 |
| #12286 | 83 |