Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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. #24923991 | C2 | semidirect |
| 2. #24923662 | C2 | semidirect |
| 4. #24923491 | C2 | semidirect |
| 6. #24923478 | C2 | semidirect |
| 7. #24923399 | C2 | semidirect |
| 8. #24923368 | C2 | semidirect |
| 9. C4×Q16×C167 | C2 | semidirect |
| 102. C167 | #3402 | semidirect |
| 112. C4×Q16 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923991 | 2 |
| #24923662 | 2 |
| #24923653 | 2 |
| #24923491 | 2 |
| #24923487 | 2 |
| #24923478 | 2 |
| #24923399 | 2 |
| #24923368 | 2 |
| C4×Q16×C167 | 2 |
| #3402 | 167 |