Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 1. #24923992 | C2 | semidirect |
| 2. #24923616 | C2 | semidirect |
| 3. #24923469 | C2 | semidirect |
| 5. #24923016 | C2 | semidirect |
| 6. #24922998 | C2 | semidirect |
| 7. Q8⋊C8×C167 | C2 | semidirect |
| 95. C167 | #1628 | semidirect |
| 102. Q8⋊C8 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923992 | 2 |
| #24923616 | 2 |
| #24923469 | 2 |
| #24923465 | 2 |
| #24923016 | 2 |
| #24922998 | 2 |
| Q8⋊C8×C167 | 2 |
| #1628 | 167 |