Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
462 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 103 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. #24916379 | C2 | semidirect |
| 3. #24909200 | C2 | semidirect |
| 4. #24908362 | C2 | semidirect |
| 5. #24905560 | C2 | semidirect |
| 6. #24905553 | C2 | semidirect |
| 7. C83×#2143 | C2 | semidirect |
| 12. C2×#14581738 | C4 | semidirect |
| 13. C2×#14581736 | C4 | semidirect |
| 14. C2×#14581735 | C4 | semidirect |
| 15. C2×#14581733 | C4 | semidirect |
| 186. #2143 | D83 | semidirect |
| 190. C83 | #13016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128131 | 2 |
| #24916379 | 2 |
| #24909200 | 2 |
| #24908362 | 2 |
| #24905560 | 2 |
| #24905553 | 2 |
| C83×#2143 | 2 |
| #13016 | 83 |