Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
386 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 91 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. #24909171 | C2 | semidirect |
| 3. #24908361 | C2 | semidirect |
| 4. #24905565 | C2 | semidirect |
| 5. C83×#2151 | C2 | semidirect |
| 111. #2151 | D83 | semidirect |
| 115. C83 | #13447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920599 | 2 |
| #24909171 | 2 |
| #24908361 | 2 |
| #24905565 | 2 |
| C83×#2151 | 2 |
| #13447 | 83 |