Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
460 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 99 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. #24907455 | C2 | semidirect |
| 3. #24906219 | C2 | semidirect |
| 4. #24906138 | C2 | semidirect |
| 5. #24905915 | C2 | semidirect |
| 6. #24905338 | C2 | semidirect |
| 7. C2×D4⋊C8×C83 | C2 | semidirect |
| 206. C2×D4⋊C8 | D83 | semidirect |
| 208. C83 | #10457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916927 | 2 |
| #24907455 | 2 |
| #24906219 | 2 |
| #24906138 | 2 |
| #24905915 | 2 |
| #24905338 | 2 |
| C2×D4⋊C8×C83 | 2 |
| #10457 | 83 |