Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 2. #24923617 | C2 | semidirect |
| 3. #24923593 | C2 | semidirect |
| 4. #24923551 | C2 | semidirect |
| 5. #24923500 | C2 | semidirect |
| 6. #24923469 | C2 | semidirect |
| 7. #24923429 | C2 | semidirect |
| 8. C4×#14581940 | C2 | semidirect |
| 9. D4×C167⋊C8 | C2 | semidirect |
| 10. #24923263 | C2 | semidirect |
| 11. #556×C167 | C2 | semidirect |
| 127. C167 | #3304 | semidirect |
| 129. #556 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923940 | 2 |
| #24923617 | 2 |
| #24923593 | 2 |
| #24923551 | 2 |
| #24923500 | 2 |
| #24923469 | 2 |
| #24923429 | 2 |
| C4×#14581940 | 2 |
| D4×C167⋊C8 | 2 |
| #24923263 | 2 |
| #556×C167 | 2 |
| #3304 | 167 |