Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
| 3. #24923618 | C2 | semidirect |
| 4. #24923552 | C2 | semidirect |
| 5. #24923551 | C2 | semidirect |
| 8. C8×Dic334 | C2 | semidirect |
| 11. #487×C167 | C2 | semidirect |
| 78. Dic334 | SD16 | semidirect |
| 118. C167 | #3359 | semidirect |
| 123. #487 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923994 | 2 |
| #24923934 | 2 |
| #24923618 | 2 |
| #24923552 | 2 |
| #24923551 | 2 |
| #24923473 | 2 |
| #24923471 | 2 |
| C8×Dic334 | 2 |
| C4×#14581939 | 2 |
| #24923354 | 2 |
| #487×C167 | 2 |
| #3359 | 167 |