Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
366 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 81 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. #24908452 | C2 | semidirect |
| 3. #24906251 | C2 | semidirect |
| 5. #24906149 | C2 | semidirect |
| 7. C83×#1299 | C2 | semidirect |
| 160. #1299 | D83 | semidirect |
| 161. C83 | #10490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918586 | 2 |
| #24908452 | 2 |
| #24906251 | 2 |
| #24906196 | 2 |
| #24906149 | 2 |
| #24905881 | 2 |
| C83×#1299 | 2 |
| #10490 | 83 |