Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D167 | C2 | semidirect |
| 3. C2×#19128808 | C2 | semidirect |
| 4. #24923524 | C2 | semidirect |
| 5. #24923512 | C2 | semidirect |
| 6. #24923507 | C2 | semidirect |
| 7. #24923495 | C2 | semidirect |
| 8. #24923311 | C2 | semidirect |
| 9. #24923278 | C2 | semidirect |
| 10. #24923270 | C2 | semidirect |
| 11. C2×#137×C167 | C2 | semidirect |
| 33. #19128766 | C22 | semidirect |
| 34. #19128764 | C22 | semidirect |
| 35. #19128756 | C22 | semidirect |
| 36. #19128756 | C22 | semidirect |
| 37. #19128756 | C22 | semidirect |
| 38. #19128753 | C22 | semidirect |
| 42. C2×Q16×C167 | C22 | semidirect |
| 43. C2×SD16×C167 | C22 | semidirect |
| 90. M16×C167 | D4 | semidirect |
| 145. C2×D167 | #137 | semidirect |
| 163. C167 | #3056 | semidirect |
| 165. C2×#137 | D167 | semidirect |
| 180. C2×Q16 | C2×D167 | semidirect |
| 181. C2×SD16 | C2×D167 | semidirect |
| 236. M16 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D167 | 2 |
| #24923776 | 2 |
| C2×#19128808 | 2 |
| #24923524 | 2 |
| #24923512 | 2 |
| #24923507 | 2 |
| #24923495 | 2 |
| #24923311 | 2 |
| #24923278 | 2 |
| #24923270 | 2 |
| C2×#137×C167 | 2 |
| #3056 | 167 |