Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
404 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 111 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. #24906222 | C2 | semidirect |
| 4. C83⋊#1309 | C2 | semidirect |
| 5. C83×#1567 | C2 | semidirect |
| 141. #1567 | D83 | semidirect |
| 144. C83 | #8638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916176 | 2 |
| #24906222 | 2 |
| #24906196 | 2 |
| C83⋊#1309 | 2 |
| C83×#1567 | 2 |
| #8638 | 83 |