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 |
|---|---|---|
| 1. #24923979 | C2 | semidirect |
| 2. #24923633 | C2 | semidirect |
| 3. #24923615 | C2 | semidirect |
| 4. #24923569 | C2 | semidirect |
| 5. #24923559 | C2 | semidirect |
| 6. #24923461 | C2 | semidirect |
| 7. #24923461 | C2 | semidirect |
| 8. #24923400 | C2 | semidirect |
| 9. #24923379 | C2 | semidirect |
| 10. C4×#14581935 | C2 | semidirect |
| 11. #550×C167 | C2 | semidirect |
| 77. D668 | #41 | semidirect |
| 129. C167 | #3366 | semidirect |
| 132. #550 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923979 | 2 |
| #24923633 | 2 |
| #24923615 | 2 |
| #24923569 | 2 |
| #24923559 | 2 |
| #24923461 | 2 |
| #24923400 | 2 |
| #24923379 | 2 |
| C4×#14581935 | 2 |
| #550×C167 | 2 |
| #3366 | 167 |