Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
216 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 79 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. #24909301 | C2 | semidirect |
| 3. #24905538 | C2 | semidirect |
| 4. #24905436 | C2 | semidirect |
| 5. #24905435 | C2 | semidirect |
| 6. C16×C83⋊C8 | C2 | semidirect |
| 7. C83×#2170 | C2 | semidirect |
| 25. #14581738 | C8 | semidirect |
| 26. #14581736 | C8 | semidirect |
| 27. #14581735 | C8 | semidirect |
| 28. #14581733 | C8 | semidirect |
| 105. #2170 | D83 | semidirect |
| 110. C83 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909342 | 2 |
| #24909301 | 2 |
| #24905538 | 2 |
| #24905436 | 2 |
| #24905435 | 2 |
| C16×C83⋊C8 | 2 |
| C83×#2170 | 2 |
| #12046 | 83 |