Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
566 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 117 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. #24909218 | C2 | semidirect |
| 3. C2×#19127515 | C2 | semidirect |
| 4. C2×#19127514 | C2 | semidirect |
| 5. C2×#19127513 | C2 | semidirect |
| 6. #108×Dic83 | C2 | semidirect |
| 7. C2×#361×C83 | C2 | semidirect |
| 47. #14581728 | D4 | semidirect |
| 65. #108×C83 | D4 | semidirect |
| 166. Dic83 | #361 | semidirect |
| 179. C2×#361 | D83 | semidirect |
| 181. C83 | #13257 | semidirect |
| 235. #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 |
| #24909218 | 2 |
| C2×#19127515 | 2 |
| C2×#19127514 | 2 |
| C2×#19127513 | 2 |
| #108×Dic83 | 2 |
| C2×#361×C83 | 2 |
| #13257 | 83 |