Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1072 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 179 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. #24918015 | C2 | semidirect |
| 3. #24917286 | C2 | semidirect |
| 4. #24913408 | C2 | semidirect |
| 5. #24908674 | C2 | semidirect |
| 6. #24908443 | C2 | semidirect |
| 7. #24907675 | C2 | semidirect |
| 8. #24907276 | C2 | semidirect |
| 9. C83×#1965 | C2 | semidirect |
| 134. M16×C83 | #41 | semidirect |
| 206. #1965 | D83 | semidirect |
| 209. C83 | #25690 | semidirect |
| 314. M16 | #13050589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24921337 | 2 |
| #24918015 | 2 |
| #24917286 | 2 |
| #24913408 | 2 |
| #24908674 | 2 |
| #24908443 | 2 |
| #24907675 | 2 |
| #24907276 | 2 |
| C83×#1965 | 2 |
| #25690 | 83 |