Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
314 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 93 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. #24909260 | C2 | semidirect |
| 3. #24909217 | C2 | semidirect |
| 4. #24905443 | C2 | semidirect |
| 5. #24905441 | C2 | semidirect |
| 6. D4⋊(C83⋊C16) | C2 | semidirect |
| 7. C83×D4⋊C16 | C2 | semidirect |
| 160. D4⋊C16 | D83 | semidirect |
| 161. C83 | #11624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916435 | 2 |
| #24909260 | 2 |
| #24909217 | 2 |
| #24905443 | 2 |
| #24905441 | 2 |
| D4⋊(C83⋊C16) | 2 |
| C83×D4⋊C16 | 2 |
| #11624 | 83 |