Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 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. #24923991 | C2 | semidirect |
| 4. #24923647 | C2 | semidirect |
| 5. #24923494 | C2 | semidirect |
| 6. #24923491 | C2 | semidirect |
| 7. #24923473 | C2 | semidirect |
| 8. C8×Dic334 | C2 | semidirect |
| 9. #24923363 | C2 | semidirect |
| 11. C4×Q16×C167 | C2 | semidirect |
| 114. C167 | #3393 | semidirect |
| 125. 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 |
| #24923654 | 2 |
| #24923653 | 2 |
| #24923647 | 2 |
| #24923494 | 2 |
| #24923491 | 2 |
| #24923473 | 2 |
| C8×Dic334 | 2 |
| #24923363 | 2 |
| #24923351 | 2 |
| C4×Q16×C167 | 2 |
| #3393 | 167 |