Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
1386 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 235 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. #24916098 | C2 | semidirect |
| 3. #24908309 | C2 | semidirect |
| 4. #24908301 | C2 | semidirect |
| 5. #24907389 | C2 | semidirect |
| 6. #24907384 | C2 | semidirect |
| 7. C83×#1783 | C2 | semidirect |
| 16. #19127724 | C22 | semidirect |
| 17. C2×#14581710 | C22 | semidirect |
| 19. C2×#14581708 | C22 | semidirect |
| 21. M16×Dic83 | C22 | semidirect |
| 165. #1783 | D83 | semidirect |
| 166. C83 | #21801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128268 | 2 |
| #24916098 | 2 |
| #24908309 | 2 |
| #24908301 | 2 |
| #24907389 | 2 |
| #24907384 | 2 |
| C83×#1783 | 2 |
| #21801 | 83 |