Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×Q16×D167 | C2 | semidirect |
| 3. #24923507 | C2 | semidirect |
| 4. #24923476 | C2 | semidirect |
| 5. #24923423 | C2 | semidirect |
| 6. C4×Dic668 | C2 | semidirect |
| 8. #494×C167 | C2 | semidirect |
| 36. Dic668 | D4 | semidirect |
| 59. D668 | Q16 | semidirect |
| 78. C2×D167 | C2×Q16 | semidirect |
| 81. C4×C167 | C2×Q16 | semidirect |
| 91. C167 | D4×Q16 | semidirect |
| 95. #494 | D167 | semidirect |
| 176. C4 | Q16×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D167 | 2 |
| #24923934 | 2 |
| #24923507 | 2 |
| #24923476 | 2 |
| #24923423 | 2 |
| C4×Dic668 | 2 |
| C8×D668 | 2 |
| #494×C167 | 2 |
| D4×Q16 | 167 |