Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
160 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 57 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. #24923564 | C2 | semidirect |
| 4. #24923020 | C2 | semidirect |
| 5. #24923017 | C2 | semidirect |
| 7. C8×Q8×C167 | C2 | semidirect |
| 76. C167 | #1678 | semidirect |
| 81. C8×Q8 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923616 | 2 |
| #24923564 | 2 |
| #24923469 | 2 |
| #24923020 | 2 |
| #24923017 | 2 |
| #24923012 | 2 |
| C8×Q8×C167 | 2 |
| #1678 | 167 |