Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
678 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 103 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. #24918773 | C2 | semidirect |
| 2. #24918381 | C2 | semidirect |
| 3. #24917913 | C2 | semidirect |
| 4. #24908381 | C2 | semidirect |
| 5. #24905957 | C2 | semidirect |
| 6. #24905313 | C2 | semidirect |
| 7. C83×#1982 | C2 | semidirect |
| 100. #13050574 | D8 | semidirect |
| 224. #1982 | D83 | semidirect |
| 228. C83 | #10192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918773 | 2 |
| #24918381 | 2 |
| #24917913 | 2 |
| #24908381 | 2 |
| #24905957 | 2 |
| #24905313 | 2 |
| C83×#1982 | 2 |
| #10192 | 83 |