Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
414 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 3. #24908444 | C2 | semidirect |
| 4. #24905937 | C2 | semidirect |
| 5. #24905356 | C2 | semidirect |
| 6. #24905354 | C2 | semidirect |
| 9. #19128111 | C4 | semidirect |
| 10. #19128096 | C4 | semidirect |
| 11. #19128071 | C4 | semidirect |
| 12. #19128060 | C4 | semidirect |
| 206. C83 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918070 | 2 |
| #24916633 | 2 |
| #24908444 | 2 |
| #24905937 | 2 |
| #24905356 | 2 |
| #24905354 | 2 |
| C83×#1500 | 2 |
| #8998 | 83 |