Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
414 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 111 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. #24909236 | C2 | semidirect |
| 3. #24909192 | C2 | semidirect |
| 4. #24909180 | C2 | semidirect |
| 5. #24908373 | C2 | semidirect |
| 6. #24908361 | C2 | semidirect |
| 7. C83×#2110 | C2 | semidirect |
| 12. C2×#14581737 | C4 | semidirect |
| 13. C2×D1328 | C4 | semidirect |
| 172. #2110 | D83 | semidirect |
| 175. C83 | #13247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128139 | 2 |
| #24909236 | 2 |
| #24909192 | 2 |
| #24909180 | 2 |
| #24908373 | 2 |
| #24908361 | 2 |
| C83×#2110 | 2 |
| #13247 | 83 |