Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
332 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #24908211 | C2 | semidirect |
| 5. #24905559 | C2 | semidirect |
| 6. #24905557 | C2 | semidirect |
| 7. C2×C4×C16×C83 | C2 | semidirect |
| 16. #19127506 | C4 | semidirect |
| 17. #19127503 | C4 | semidirect |
| 140. C2×C4×C16 | 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×#19127509 | 2 |
| #24909171 | 2 |
| #24908351 | 2 |
| #24908211 | 2 |
| #24905559 | 2 |
| #24905557 | 2 |
| C2×C4×C16×C83 | 2 |
| #13151 | 83 |