Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
650 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#19128139 | C2 | semidirect |
| 2. C2×#19128137 | C2 | semidirect |
| 3. C2×#19128076 | C2 | semidirect |
| 4. C2×#19127513 | C2 | semidirect |
| 5. #24908349 | C2 | semidirect |
| 6. #24905544 | C2 | semidirect |
| 7. C2×#361×C83 | C2 | semidirect |
| 38. C2×Dic332 | D4 | semidirect |
| 46. C2×D664 | D4 | semidirect |
| 59. #14581732 | D4 | semidirect |
| 75. M32×C83 | D4 | semidirect |
| 210. C2×#361 | D83 | semidirect |
| 213. C83 | #13331 | semidirect |
| 276. M32 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128139 | 2 |
| C2×#19128137 | 2 |
| C2×#19128076 | 2 |
| C2×#19127513 | 2 |
| #24908349 | 2 |
| #24905544 | 2 |
| C2×#361×C83 | 2 |
| #13331 | 83 |