Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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×#19127507 | C2 | semidirect |
| 3. #24909176 | C2 | semidirect |
| 4. C2×#19127502 | C2 | semidirect |
| 5. #24908249 | C2 | semidirect |
| 6. #24905553 | C2 | semidirect |
| 7. C2×#361×C83 | C2 | semidirect |
| 69. #108×C83 | D4 | semidirect |
| 191. C2×#361 | D83 | semidirect |
| 197. C83 | #13411 | semidirect |
| 253. #108 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917944 | 2 |
| C2×#19127507 | 2 |
| #24909176 | 2 |
| C2×#19127502 | 2 |
| #24908249 | 2 |
| #24905553 | 2 |
| C2×#361×C83 | 2 |
| #13411 | 83 |