Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
540 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 540 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. C2×#19127513 | C2 | semidirect |
| 3. #24909180 | C2 | semidirect |
| 4. #24909179 | C2 | semidirect |
| 5. #24908209 | C2 | semidirect |
| 6. #24905544 | C2 | semidirect |
| 7. C2×#361×C83 | C2 | semidirect |
| 44. #14581726 | D4 | semidirect |
| 169. C2×#361 | D83 | semidirect |
| 174. C83 | #13413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128076 | 2 |
| C2×#19127513 | 2 |
| #24909180 | 2 |
| #24909179 | 2 |
| #24908209 | 2 |
| #24905544 | 2 |
| C2×#361×C83 | 2 |
| #13413 | 83 |