Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
390 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. #24909720 | C2 | semidirect |
| 2. #24909498 | C2 | semidirect |
| 3. #24906818 | C2 | semidirect |
| 4. #24905512 | C2 | semidirect |
| 5. #24905424 | C2 | semidirect |
| 6. D4⋊(C83⋊C16) | C2 | semidirect |
| 7. C83×#3283 | C2 | semidirect |
| 80. D8×C83 | D8 | semidirect |
| 151. #3283 | D83 | semidirect |
| 158. C83 | #12319 | semidirect |
| 228. D8 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909720 | 2 |
| #24909498 | 2 |
| #24906818 | 2 |
| #24905512 | 2 |
| #24905424 | 2 |
| D4⋊(C83⋊C16) | 2 |
| C83×#3283 | 2 |
| #12319 | 83 |