Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
636 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 636 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. #24917908 | C2 | semidirect |
| 2. #24917463 | C2 | semidirect |
| 3. #24908262 | C2 | semidirect |
| 4. #24905863 | C2 | semidirect |
| 5. #24905862 | C2 | semidirect |
| 6. #24905293 | C2 | semidirect |
| 7. C83×#3100 | C2 | semidirect |
| 103. C2×C83⋊C8 | D8 | semidirect |
| 224. #3100 | D83 | semidirect |
| 229. C83 | #10032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917908 | 2 |
| #24917463 | 2 |
| #24908262 | 2 |
| #24905863 | 2 |
| #24905862 | 2 |
| #24905293 | 2 |
| C83×#3100 | 2 |
| #10032 | 83 |