Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
298 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 147 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. #24905385 | C2 | semidirect |
| 5. #24905384 | C2 | semidirect |
| 6. #24905383 | C2 | semidirect |
| 7. C83×#1313 | C2 | semidirect |
| 26. #14581731 | C8 | semidirect |
| 49. C83⋊C16 | C2×C8 | semidirect |
| 55. C16×C83 | C2×C8 | semidirect |
| 88. #1313 | D83 | semidirect |
| 89. C83 | #11404 | semidirect |
| 137. C16 | C8×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909056 | 2 |
| #322×D83 | 2 |
| #24905385 | 2 |
| #24905384 | 2 |
| #24905383 | 2 |
| C83×#1313 | 2 |
| #11404 | 83 |