Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
554 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 554 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 |
|---|---|---|
| 1. #24908697 | C2 | semidirect |
| 2. #24908550 | C2 | semidirect |
| 4. #24905289 | C2 | semidirect |
| 5. #24905286 | C2 | semidirect |
| 6. #24905284 | C2 | semidirect |
| 7. C83×#2808 | C2 | semidirect |
| 232. #2808 | D83 | semidirect |
| 239. C83 | #7746 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24908697 | 2 |
| #24908550 | 2 |
| #24908533 | 2 |
| #24905289 | 2 |
| #24905286 | 2 |
| #24905284 | 2 |
| C83×#2808 | 2 |
| #7746 | 83 |