Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
284 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 2. #24909783 | C2 | semidirect |
| 3. #24909780 | C2 | semidirect |
| 4. #24909572 | C2 | semidirect |
| 5. #24905649 | C2 | semidirect |
| 6. #24905602 | C2 | semidirect |
| 7. C83×#1418 | C2 | semidirect |
| 15. C2×Dic664 | C22 | semidirect |
| 22. #19127535 | C22 | semidirect |
| 25. M64×C83 | C22 | semidirect |
| 26. #367×C83 | C22 | semidirect |
| 146. #1418 | D83 | semidirect |
| 148. C83 | #13668 | semidirect |
| 165. M64 | C2×D83 | semidirect |
| 166. #367 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920596 | 2 |
| #24909783 | 2 |
| #24909780 | 2 |
| #24909572 | 2 |
| #24905649 | 2 |
| #24905602 | 2 |
| C83×#1418 | 2 |
| #13668 | 83 |