Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #24923607 | C2 | semidirect |
| 3. #24923561 | C2 | semidirect |
| 4. #24923556 | C2 | semidirect |
| 5. #24923476 | C2 | semidirect |
| 6. #24923471 | C2 | semidirect |
| 8. #24923374 | C2 | semidirect |
| 9. #24923367 | C2 | semidirect |
| 10. #24923326 | C2 | semidirect |
| 11. #533×C167 | C2 | semidirect |
| 136. C167 | #3116 | semidirect |
| 138. #533 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14581950 | 2 |
| #24923607 | 2 |
| #24923561 | 2 |
| #24923556 | 2 |
| #24923476 | 2 |
| #24923471 | 2 |
| #24923429 | 2 |
| #24923374 | 2 |
| #24923367 | 2 |
| #24923326 | 2 |
| #533×C167 | 2 |
| #3116 | 167 |