Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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. #24908416 | C2 | semidirect |
| 3. #24906189 | C2 | semidirect |
| 5. #24905332 | C2 | semidirect |
| 6. #24905318 | C2 | semidirect |
| 26. #501×C83 | C4 | semidirect |
| 27. #489×C83 | C4 | semidirect |
| 196. C83 | #9375 | semidirect |
| 199. #501 | Dic83 | semidirect |
| 200. #489 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916602 | 2 |
| #24908416 | 2 |
| #24906189 | 2 |
| #24905988 | 2 |
| #24905332 | 2 |
| #24905318 | 2 |
| C83×#3238 | 2 |
| #9375 | 83 |