Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
634 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 101 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. #24918770 | C2 | semidirect |
| 2. #24916929 | C2 | semidirect |
| 3. #24916923 | C2 | semidirect |
| 4. #24908257 | C2 | semidirect |
| 5. #24905915 | C2 | semidirect |
| 6. #24905337 | C2 | semidirect |
| 7. C83×#1492 | C2 | semidirect |
| 101. C2×D332 | D8 | semidirect |
| 254. #1492 | D83 | semidirect |
| 256. C83 | #10254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918770 | 2 |
| #24916929 | 2 |
| #24916923 | 2 |
| #24908257 | 2 |
| #24905915 | 2 |
| #24905337 | 2 |
| C83×#1492 | 2 |
| #10254 | 83 |