Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
340 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 137 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. #24923677 | C2 | semidirect |
| 3. #24923675 | C2 | semidirect |
| 4. #24923673 | C2 | semidirect |
| 5. #24923671 | C2 | semidirect |
| 6. #24923670 | C2 | semidirect |
| 11. #500×C167 | C2 | semidirect |
| 42. #14581933 | Q8 | semidirect |
| 45. C8×D167 | Q8 | semidirect |
| 107. C167 | #3164 | semidirect |
| 113. #500 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923896 | 2 |
| #24923677 | 2 |
| #24923675 | 2 |
| #24923673 | 2 |
| #24923671 | 2 |
| #24923670 | 2 |
| #24923310 | 2 |
| #24923306 | 2 |
| #107×D167 | 2 |
| #24923223 | 2 |
| #500×C167 | 2 |
| #3164 | 167 |