Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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. #24909775 | C2 | semidirect |
| 2. #24909711 | C2 | semidirect |
| 3. #24909344 | C2 | semidirect |
| 4. #24905660 | C2 | semidirect |
| 5. #24905654 | C2 | semidirect |
| 6. #24905653 | C2 | semidirect |
| 7. C83×#2263 | C2 | semidirect |
| 37. Q32×C83 | D4 | semidirect |
| 41. D16×C83 | D4 | semidirect |
| 101. #2263 | D83 | semidirect |
| 107. C83 | #13692 | semidirect |
| 129. Q32 | C22⋊D83 | semidirect |
| 136. D16 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909775 | 2 |
| #24909711 | 2 |
| #24909344 | 2 |
| #24905660 | 2 |
| #24905654 | 2 |
| #24905653 | 2 |
| C83×#2263 | 2 |
| #13692 | 83 |