Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
| 4. #24923528 | C2 | semidirect |
| 5. #24923527 | C2 | semidirect |
| 6. #24923524 | C2 | semidirect |
| 7. #24923509 | C2 | semidirect |
| 8. #24923508 | C2 | semidirect |
| 9. #24923304 | C2 | semidirect |
| 10. #24923276 | C2 | semidirect |
| 11. #470×C167 | C2 | semidirect |
| 133. C167 | #3059 | semidirect |
| 141. #470 | 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 |
| C2×#19128840 | 2 |
| #24923842 | 2 |
| #24923528 | 2 |
| #24923527 | 2 |
| #24923524 | 2 |
| #24923509 | 2 |
| #24923508 | 2 |
| #24923304 | 2 |
| #24923276 | 2 |
| #470×C167 | 2 |
| #3059 | 167 |