Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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. #24907612 | C2 | semidirect |
| 3. #24905458 | C2 | semidirect |
| 5. #24905452 | C2 | semidirect |
| 7. C83×#2165 | C2 | semidirect |
| 9. #19128103 | C4 | semidirect |
| 10. #19128085 | C4 | semidirect |
| 15. #19127814 | C4 | semidirect |
| 16. #19127809 | C4 | semidirect |
| 141. #2165 | D83 | semidirect |
| 147. C83 | #11836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918192 | 2 |
| #24907612 | 2 |
| #24905458 | 2 |
| #24905455 | 2 |
| #24905452 | 2 |
| #24905449 | 2 |
| C83×#2165 | 2 |
| #11836 | 83 |