Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
394 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24909259 | C2 | semidirect |
| 3. #24907355 | C2 | semidirect |
| 4. #24905473 | C2 | semidirect |
| 5. #24905472 | C2 | semidirect |
| 6. #24905471 | C2 | semidirect |
| 7. C83×#1347 | C2 | semidirect |
| 9. #19128105 | C4 | semidirect |
| 10. #19128076 | C4 | semidirect |
| 14. D8×Dic83 | C4 | semidirect |
| 15. #19127783 | C4 | semidirect |
| 179. #1347 | D83 | semidirect |
| 180. C83 | #11742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918037 | 2 |
| #24909259 | 2 |
| #24907355 | 2 |
| #24905473 | 2 |
| #24905472 | 2 |
| #24905471 | 2 |
| C83×#1347 | 2 |
| #11742 | 83 |