Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 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. #24923994 | C2 | semidirect |
| 4. #24923574 | C2 | semidirect |
| 7. #24923476 | C2 | semidirect |
| 8. C8×Dic334 | C2 | semidirect |
| 9. #24923361 | C2 | semidirect |
| 11. #487×C167 | C2 | semidirect |
| 115. C167 | #3364 | semidirect |
| 120. #487 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923994 | 2 |
| #24923993 | 2 |
| #24923625 | 2 |
| #24923574 | 2 |
| #24923546 | 2 |
| #24923494 | 2 |
| #24923476 | 2 |
| C8×Dic334 | 2 |
| #24923361 | 2 |
| C4×#14581939 | 2 |
| #487×C167 | 2 |
| #3364 | 167 |