Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
456 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 3. C2×#19128107 | C2 | semidirect |
| 5. #24905820 | C2 | semidirect |
| 6. #24905361 | C2 | semidirect |
| 7. C83×#1558 | C2 | semidirect |
| 172. #1558 | D83 | semidirect |
| 176. C83 | #10142 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918655 | 2 |
| #24918584 | 2 |
| C2×#19128107 | 2 |
| #24906075 | 2 |
| #24905820 | 2 |
| #24905361 | 2 |
| C83×#1558 | 2 |
| #10142 | 83 |