Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 99 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×#19127516 | C2 | semidirect |
| 4. #24909182 | C2 | semidirect |
| 6. #24905545 | C2 | semidirect |
| 7. C83×#1945 | C2 | semidirect |
| 165. #1945 | D83 | semidirect |
| 167. C83 | #13414 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128085 | 2 |
| C2×#19127516 | 2 |
| C2×#19127513 | 2 |
| #24909182 | 2 |
| #24909178 | 2 |
| #24905545 | 2 |
| C83×#1945 | 2 |
| #13414 | 83 |