Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
374 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 69 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. #24909715 | C2 | semidirect |
| 3. #24909505 | C2 | semidirect |
| 4. #24905511 | C2 | semidirect |
| 5. #24905423 | C2 | semidirect |
| 6. D4⋊(C83⋊C16) | C2 | semidirect |
| 7. C83×#1669 | C2 | semidirect |
| 147. #1669 | D83 | semidirect |
| 151. C83 | #12323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24919185 | 2 |
| #24909715 | 2 |
| #24909505 | 2 |
| #24905511 | 2 |
| #24905423 | 2 |
| D4⋊(C83⋊C16) | 2 |
| C83×#1669 | 2 |
| #12323 | 83 |