Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
578 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 1. #24918037 | C2 | semidirect |
| 2. #24909599 | C2 | semidirect |
| 3. #24909598 | C2 | semidirect |
| 4. #24909549 | C2 | semidirect |
| 5. #24909547 | C2 | semidirect |
| 6. #24909497 | C2 | semidirect |
| 7. #24909496 | C2 | semidirect |
| 8. C2×Dic83⋊C16 | C2 | semidirect |
| 9. C83×#2215 | C2 | semidirect |
| 121. C2×Dic83 | D16 | semidirect |
| 161. #2215 | D83 | semidirect |
| 165. C83 | #33811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918037 | 2 |
| #24909599 | 2 |
| #24909598 | 2 |
| #24909549 | 2 |
| #24909547 | 2 |
| #24909497 | 2 |
| #24909496 | 2 |
| C2×Dic83⋊C16 | 2 |
| C83×#2215 | 2 |
| #33811 | 83 |