Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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. C2×#19127521 | C2 | semidirect |
| 3. C2×#19127513 | C2 | semidirect |
| 4. #24909180 | C2 | semidirect |
| 5. #24909179 | C2 | semidirect |
| 6. #24907345 | C2 | semidirect |
| 7. C2×#361×C83 | C2 | semidirect |
| 13. #19128076 | C4 | semidirect |
| 46. #14581726 | D4 | semidirect |
| 65. #108×C83 | D4 | semidirect |
| 176. C2×#361 | D83 | semidirect |
| 180. C83 | #13261 | semidirect |
| 232. #108 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128076 | 2 |
| C2×#19127521 | 2 |
| C2×#19127513 | 2 |
| #24909180 | 2 |
| #24909179 | 2 |
| #24907345 | 2 |
| C2×#361×C83 | 2 |
| #13261 | 83 |