Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 3. #24923565 | C2 | semidirect |
| 4. #24923564 | C2 | semidirect |
| 6. #24923001 | C2 | semidirect |
| 7. Q8⋊C8×C167 | C2 | semidirect |
| 89. C167 | #1630 | semidirect |
| 97. Q8⋊C8 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924004 | 2 |
| #24923642 | 2 |
| #24923565 | 2 |
| #24923564 | 2 |
| #24923012 | 2 |
| #24923001 | 2 |
| Q8⋊C8×C167 | 2 |
| #1630 | 167 |