Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
| 3. #24923493 | C2 | semidirect |
| 4. #24923471 | C2 | semidirect |
| 5. C8×Dic334 | C2 | semidirect |
| 6. Q16×Dic167 | C2 | semidirect |
| 8. #494×C167 | C2 | semidirect |
| 84. C167 | #3393 | semidirect |
| 88. #494 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923993 | 2 |
| #24923654 | 2 |
| #24923493 | 2 |
| #24923471 | 2 |
| C8×Dic334 | 2 |
| Q16×Dic167 | 2 |
| C4×D1336 | 2 |
| #494×C167 | 2 |
| #3393 | 167 |