Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
188 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 51 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. C2×#19127536 | C2 | semidirect |
| 2. #24909758 | C2 | semidirect |
| 3. #24909584 | C2 | semidirect |
| 4. #24909580 | C2 | semidirect |
| 5. #24905666 | C2 | semidirect |
| 6. #24905654 | C2 | semidirect |
| 7. C83×#1419 | C2 | semidirect |
| 100. #1419 | D83 | semidirect |
| 101. C83 | #13700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127536 | 2 |
| #24909758 | 2 |
| #24909584 | 2 |
| #24909580 | 2 |
| #24905666 | 2 |
| #24905654 | 2 |
| C83×#1419 | 2 |
| #13700 | 83 |