Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×C4×Dic334 | C2 | semidirect |
| 3. #24923583 | C2 | semidirect |
| 4. #24923565 | C2 | semidirect |
| 5. #24923470 | C2 | semidirect |
| 6. #24923410 | C2 | semidirect |
| 7. #24923371 | C2 | semidirect |
| 8. #432×C167 | C2 | semidirect |
| 68. Dic334 | #41 | semidirect |
| 111. C167 | #3112 | semidirect |
| 120. #432 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923819 | 2 |
| C2×C4×Dic334 | 2 |
| #24923583 | 2 |
| #24923565 | 2 |
| #24923470 | 2 |
| #24923410 | 2 |
| #24923371 | 2 |
| #432×C167 | 2 |
| #3112 | 167 |