Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
512 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24917586 | C2 | semidirect |
| 3. #24917581 | C2 | semidirect |
| 4. #24908403 | C2 | semidirect |
| 5. #24906073 | C2 | semidirect |
| 6. #24905332 | C2 | semidirect |
| 7. C83×#1530 | C2 | semidirect |
| 207. #1530 | D83 | semidirect |
| 209. C83 | #10028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918770 | 2 |
| #24917586 | 2 |
| #24917581 | 2 |
| #24908403 | 2 |
| #24906073 | 2 |
| #24905332 | 2 |
| C83×#1530 | 2 |
| #10028 | 83 |