Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. #24923993 | C2 | semidirect |
| 2. #24923980 | C2 | semidirect |
| 3. #24923625 | C2 | semidirect |
| 4. #24923578 | C2 | semidirect |
| 5. #24923556 | C2 | semidirect |
| 7. #24923471 | C2 | semidirect |
| 8. C8×Dic334 | C2 | semidirect |
| 9. #24923354 | C2 | semidirect |
| 11. #487×C167 | C2 | semidirect |
| 120. C167 | #3360 | semidirect |
| 125. #487 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923993 | 2 |
| #24923980 | 2 |
| #24923625 | 2 |
| #24923578 | 2 |
| #24923556 | 2 |
| #24923487 | 2 |
| #24923471 | 2 |
| C8×Dic334 | 2 |
| #24923354 | 2 |
| C4×D1336 | 2 |
| #487×C167 | 2 |
| #3360 | 167 |