Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
476 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19128864 | C2 | semidirect |
| 2. #24923931 | C2 | semidirect |
| 3. #24923653 | C2 | semidirect |
| 4. #24923516 | C2 | semidirect |
| 5. #24923491 | C2 | semidirect |
| 6. #24923426 | C2 | semidirect |
| 7. #24923417 | C2 | semidirect |
| 8. #24923348 | C2 | semidirect |
| 9. C4×Q16×C167 | C2 | semidirect |
| 64. Q16×C167 | D4 | semidirect |
| 117. C167 | #3277 | semidirect |
| 126. C4×Q16 | D167 | semidirect |
| 170. Q16 | D668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128864 | 2 |
| #24923931 | 2 |
| #24923653 | 2 |
| #24923516 | 2 |
| #24923491 | 2 |
| #24923426 | 2 |
| #24923417 | 2 |
| #24923348 | 2 |
| C4×Q16×C167 | 2 |
| #3277 | 167 |