Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
442 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 151 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. C4×#14581728 | C2 | semidirect |
| 4. #24905559 | C2 | semidirect |
| 5. C2×#346×C83 | C2 | semidirect |
| 15. #19127509 | C4 | semidirect |
| 34. #14581728 | C2×C4 | semidirect |
| 46. C2×C16×C83 | C2×C4 | semidirect |
| 124. C2×#346 | D83 | semidirect |
| 127. C83 | #12640 | semidirect |
| 160. C2×C16 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14581814 | 2 |
| C2×#19127509 | 2 |
| C4×#14581728 | 2 |
| #24905559 | 2 |
| C2×#346×C83 | 2 |
| #12640 | 83 |