Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
394 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 394 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. #24908306 | C2 | semidirect |
| 3. #24906254 | C2 | semidirect |
| 4. #24906145 | C2 | semidirect |
| 6. #24905352 | C2 | semidirect |
| 166. C83 | #10489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918385 | 2 |
| #24908306 | 2 |
| #24906254 | 2 |
| #24906145 | 2 |
| #24905880 | 2 |
| #24905352 | 2 |
| C83×#1560 | 2 |
| #10489 | 83 |