Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
926 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 926 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#19127515 | C2 | semidirect |
| 3. #24909192 | C2 | semidirect |
| 4. #24907513 | C2 | semidirect |
| 5. C83×#2115 | C2 | semidirect |
| 15. C2×#14581728 | C22 | semidirect |
| 21. C2×M32×C83 | C22 | semidirect |
| 178. #2115 | D83 | semidirect |
| 180. C83 | #12743 | semidirect |
| 191. C2×M32 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128506 | 2 |
| C2×#19127515 | 2 |
| #24909192 | 2 |
| #24907513 | 2 |
| C83×#2115 | 2 |
| #12743 | 83 |