Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
394 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 115 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. #24909236 | C2 | semidirect |
| 3. #24909183 | C2 | semidirect |
| 4. #24909067 | C2 | semidirect |
| 5. #24908379 | C2 | semidirect |
| 24. C2×Q32×C83 | C4 | semidirect |
| 25. C2×SD32×C83 | C4 | semidirect |
| 170. C83 | #13248 | semidirect |
| 175. C2×Q32 | Dic83 | semidirect |
| 176. C2×SD32 | Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909236 | 2 |
| #24909191 | 2 |
| #24909183 | 2 |
| #24909067 | 2 |
| #24908379 | 2 |
| #24908362 | 2 |
| C2×#510×C83 | 2 |
| #13248 | 83 |