Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
554 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 554 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. #24908292 | C2 | semidirect |
| 2. C4×C8×Dic83 | C2 | semidirect |
| 3. #24906222 | C2 | semidirect |
| 4. #24905914 | C2 | semidirect |
| 14. #500×C83 | C4 | semidirect |
| 15. #493×C83 | C4 | semidirect |
| 16. #486×C83 | C4 | semidirect |
| 55. C4×Dic83 | D8 | semidirect |
| 103. C8×C83 | #104 | semidirect |
| 133. C83 | #9844 | semidirect |
| 135. #500 | Dic83 | semidirect |
| 136. #493 | Dic83 | semidirect |
| 137. #486 | Dic83 | semidirect |
| 233. C8 | #14581719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24908292 | 2 |
| C4×C8×Dic83 | 2 |
| #24906222 | 2 |
| #24905914 | 2 |
| C83×#3169 | 2 |
| #9844 | 83 |