Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
320 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 89 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. #24909263 | C2 | semidirect |
| 3. #24909259 | C2 | semidirect |
| 4. #24905403 | C2 | semidirect |
| 7. C83×#1322 | C2 | semidirect |
| 163. #1322 | D83 | semidirect |
| 166. C83 | #11461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127761 | 2 |
| #24909263 | 2 |
| #24909259 | 2 |
| #24905403 | 2 |
| #24905386 | 2 |
| C83×#1322 | 2 |
| #11461 | 83 |