Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
348 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 73 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. #24907603 | C2 | semidirect |
| 3. #24906194 | C2 | semidirect |
| 5. #24906079 | C2 | semidirect |
| 7. C83×#1307 | C2 | semidirect |
| 160. #1307 | D83 | semidirect |
| 161. C83 | #10527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918851 | 2 |
| #24907603 | 2 |
| #24906194 | 2 |
| #24906186 | 2 |
| #24906079 | 2 |
| #24906075 | 2 |
| C83×#1307 | 2 |
| #10527 | 83 |