Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
296 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 87 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. #24909690 | C2 | semidirect |
| 4. #24905381 | C2 | semidirect |
| 5. C83×#1713 | C2 | semidirect |
| 64. C8×C83 | SD32 | semidirect |
| 82. #1713 | D83 | semidirect |
| 85. C83 | #12526 | semidirect |
| 144. C8 | #14581735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909720 | 2 |
| #24909690 | 2 |
| #24907055 | 2 |
| #24905381 | 2 |
| C83×#1713 | 2 |
| #12526 | 83 |