Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
394 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 109 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. #24909235 | C2 | semidirect |
| 3. C2×#19127524 | C2 | semidirect |
| 6. #24905568 | C2 | semidirect |
| 7. C83×#1384 | C2 | semidirect |
| 21. #19127484 | C4 | semidirect |
| 42. #14581732 | C2×C4 | semidirect |
| 56. C2×C16×C83 | C2×C4 | semidirect |
| 159. #1384 | D83 | semidirect |
| 160. C83 | #12934 | semidirect |
| 202. C2×C16 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916055 | 2 |
| #24909235 | 2 |
| C2×#19127524 | 2 |
| #24909090 | 2 |
| #24907514 | 2 |
| #24905568 | 2 |
| C83×#1384 | 2 |
| #12934 | 83 |