Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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. #24924005 | C2 | semidirect |
| 2. #24923940 | C2 | semidirect |
| 3. #24923657 | C2 | semidirect |
| 4. #24923645 | C2 | semidirect |
| 5. #24923483 | C2 | semidirect |
| 6. #24923470 | C2 | semidirect |
| 7. #24923462 | C2 | semidirect |
| 8. #24923396 | C2 | semidirect |
| 9. #24923378 | C2 | semidirect |
| 10. C4×#14581938 | C2 | semidirect |
| 11. #459×C167 | C2 | semidirect |
| 94. C167⋊C8 | #41 | semidirect |
| 134. C167 | #3399 | semidirect |
| 143. #459 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924005 | 2 |
| #24923940 | 2 |
| #24923657 | 2 |
| #24923645 | 2 |
| #24923483 | 2 |
| #24923470 | 2 |
| #24923462 | 2 |
| #24923396 | 2 |
| #24923378 | 2 |
| C4×#14581938 | 2 |
| #459×C167 | 2 |
| #3399 | 167 |