Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 2. #24923602 | C2 | semidirect |
| 3. #24923546 | C2 | semidirect |
| 4. #24923471 | C2 | semidirect |
| 6. #24923367 | C2 | semidirect |
| 7. #24923326 | C2 | semidirect |
| 8. #533×C167 | C2 | semidirect |
| 18. #19128765 | C22 | semidirect |
| 19. C4⋊(C167⋊C8) | C22 | semidirect |
| 20. #19128756 | C22 | semidirect |
| 23. #19128743 | C22 | semidirect |
| 24. C4⋊Q8×C167 | C22 | semidirect |
| 25. C4⋊Q8×C167 | C22 | semidirect |
| 30. C4×Q8×C167 | C22 | semidirect |
| 112. C167 | #3110 | semidirect |
| 114. #533 | D167 | semidirect |
| 125. C4⋊Q8 | C2×D167 | semidirect |
| 126. C4⋊Q8 | C2×D167 | semidirect |
| 131. C4×Q8 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D668 | 2 |
| #24923602 | 2 |
| #24923546 | 2 |
| #24923471 | 2 |
| #24923419 | 2 |
| #24923367 | 2 |
| #24923326 | 2 |
| #533×C167 | 2 |
| #3110 | 167 |