Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 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. #24920597 | C2 | semidirect |
| 2. C2×#19128137 | C2 | semidirect |
| 3. #24909199 | C2 | semidirect |
| 4. #24909179 | C2 | semidirect |
| 5. #24908361 | C2 | semidirect |
| 6. #24905549 | C2 | semidirect |
| 7. C83×#3155 | C2 | semidirect |
| 38. C2×Dic332 | D4 | semidirect |
| 40. C2×D664 | D4 | semidirect |
| 51. #14581732 | D4 | semidirect |
| 53. C2×C83⋊C16 | D4 | semidirect |
| 220. #3155 | D83 | semidirect |
| 225. C83 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920597 | 2 |
| C2×#19128137 | 2 |
| #24909199 | 2 |
| #24909179 | 2 |
| #24908361 | 2 |
| #24905549 | 2 |
| C83×#3155 | 2 |
| #13334 | 83 |