Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
726 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 199 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. #24908268 | C2 | semidirect |
| 3. C2×C8×C83⋊C8 | C2 | semidirect |
| 4. C83×#1845 | C2 | semidirect |
| 8. #19128078 | C4 | semidirect |
| 46. C2×C83⋊C8 | D8 | semidirect |
| 78. C8×C83 | #102 | semidirect |
| 104. #1845 | D83 | semidirect |
| 106. C83 | #9824 | semidirect |
| 181. C8 | #14581712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128078 | 2 |
| #24908268 | 2 |
| C2×C8×C83⋊C8 | 2 |
| C83×#1845 | 2 |
| #9824 | 83 |