Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
302 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 61 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. #24920039 | C2 | semidirect |
| 2. #24909705 | C2 | semidirect |
| 3. #24909503 | C2 | semidirect |
| 5. #24905516 | C2 | semidirect |
| 6. #24905422 | C2 | semidirect |
| 7. C83×#1334 | C2 | semidirect |
| 152. #1334 | D83 | semidirect |
| 154. C83 | #12349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920039 | 2 |
| #24909705 | 2 |
| #24909503 | 2 |
| #24906943 | 2 |
| #24905516 | 2 |
| #24905422 | 2 |
| C83×#1334 | 2 |
| #12349 | 83 |