Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
410 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. #24905414 | C2 | semidirect |
| 4. #24905413 | C2 | semidirect |
| 5. C83×#1327 | C2 | semidirect |
| 158. D83 | #1327 | direct (N × H) |
| 163. #1327 | D83 | direct (N × H) |
| 164. C83 | C2×#1327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #423×D83 | 2 |
| #349×D83 | 2 |
| #24905414 | 2 |
| #24905413 | 2 |
| C83×#1327 | 2 |
| C2×#1327 | 83 |