Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
520 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 93 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. #24920597 | C2 | semidirect |
| 2. #24917184 | C2 | semidirect |
| 3. #24917179 | C2 | semidirect |
| 4. C2×#19127509 | C2 | semidirect |
| 5. #24909076 | C2 | semidirect |
| 6. #24905566 | C2 | semidirect |
| 7. C2×#359×C83 | C2 | semidirect |
| 227. C2×#359 | D83 | semidirect |
| 230. C83 | #13312 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920597 | 2 |
| #24917184 | 2 |
| #24917179 | 2 |
| C2×#19127509 | 2 |
| #24909076 | 2 |
| #24905566 | 2 |
| C2×#359×C83 | 2 |
| #13312 | 83 |