Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
332 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. C2×C4×C83⋊C16 | C2 | semidirect |
| 5. #24905558 | C2 | semidirect |
| 6. #24905556 | C2 | semidirect |
| 7. C83×#1945 | C2 | semidirect |
| 15. #19127504 | C4 | semidirect |
| 16. #19127501 | C4 | semidirect |
| 142. #1945 | D83 | semidirect |
| 145. C83 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127507 | 2 |
| #24909168 | 2 |
| C2×C4×C83⋊C16 | 2 |
| #24908351 | 2 |
| #24905558 | 2 |
| #24905556 | 2 |
| C83×#1945 | 2 |
| #13151 | 83 |