Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. #24923647 | C2 | semidirect |
| 4. #24923510 | C2 | semidirect |
| 5. #24923507 | C2 | semidirect |
| 6. #24923477 | C2 | semidirect |
| 7. #24923425 | C2 | semidirect |
| 8. #24923423 | C2 | semidirect |
| 9. Q16×Dic167 | C2 | semidirect |
| 11. C22×Q16×C167 | C2 | semidirect |
| 76. Q16×C167 | D4 | semidirect |
| 84. C22⋊D167 | Q16 | direct (N × H) |
| 112. C22×C167 | C2×Q16 | semidirect |
| 116. C2×D167 | C2×Q16 | semidirect |
| 126. Dic167 | C2×Q16 | semidirect |
| 132. C167 | D4×Q16 | semidirect |
| 135. C22×Q16 | D167 | semidirect |
| 193. Q16 | C22⋊D167 | direct (N × H) |
| 248. C22 | 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 |
| Q8×C22⋊D167 | 2 |
| #24923647 | 2 |
| #24923510 | 2 |
| #24923507 | 2 |
| #24923477 | 2 |
| #24923425 | 2 |
| #24923423 | 2 |
| Q16×Dic167 | 2 |
| C8×C22⋊D167 | 2 |
| C22×Q16×C167 | 2 |
| D4×Q16 | 167 |