Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
346 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24907603 | C2 | semidirect |
| 5. #24905321 | C2 | semidirect |
| 6. #24905307 | C2 | semidirect |
| 7. C83×#1286 | C2 | semidirect |
| 153. #1286 | D83 | semidirect |
| 155. C83 | #10634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24908286 | 2 |
| #24907603 | 2 |
| #24906132 | 2 |
| #24906130 | 2 |
| #24905321 | 2 |
| #24905307 | 2 |
| C83×#1286 | 2 |
| #10634 | 83 |