Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
678 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 678 conjugacy classes of subgroups — too many to draw. Only its 105 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. #24918378 | C2 | semidirect |
| 2. #24917916 | C2 | semidirect |
| 3. #24908389 | C2 | semidirect |
| 4. #24908383 | C2 | semidirect |
| 5. #24905958 | C2 | semidirect |
| 6. #24905313 | C2 | semidirect |
| 7. C83×#3245 | C2 | semidirect |
| 96. #13050574 | D8 | semidirect |
| 221. #3245 | 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 |
|---|---|
| #24918378 | 2 |
| #24917916 | 2 |
| #24908389 | 2 |
| #24908383 | 2 |
| #24905958 | 2 |
| #24905313 | 2 |
| C83×#3245 | 2 |
| #10192 | 83 |