Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
472 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 93 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. #24908184 | C2 | semidirect |
| 3. #24906113 | C2 | semidirect |
| 4. #24905959 | C2 | semidirect |
| 5. #24905958 | C2 | semidirect |
| 6. #24905293 | C2 | semidirect |
| 7. C83×#1540 | C2 | semidirect |
| 219. #1540 | D83 | semidirect |
| 223. C83 | #10546 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24917908 | 2 |
| #24908184 | 2 |
| #24906113 | 2 |
| #24905959 | 2 |
| #24905958 | 2 |
| #24905293 | 2 |
| C83×#1540 | 2 |
| #10546 | 83 |