Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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. #24923924 | C2 | semidirect |
| 2. #24923904 | C2 | semidirect |
| 3. #24923615 | C2 | semidirect |
| 4. #24923581 | C2 | semidirect |
| 5. #24923550 | C2 | semidirect |
| 6. #24923502 | C2 | semidirect |
| 7. #24923401 | C2 | semidirect |
| 8. C4×#14581935 | C2 | semidirect |
| 9. #24923334 | C2 | semidirect |
| 10. #102×D167 | C2 | semidirect |
| 11. #459×C167 | C2 | semidirect |
| 16. C2×C8×D167 | C22 | semidirect |
| 17. #19128832 | C22 | semidirect |
| 22. #19128803 | C22 | semidirect |
| 26. C4⋊C4×D167 | C22 | semidirect |
| 27. #19128766 | C22 | semidirect |
| 28. #19128765 | C22 | semidirect |
| 30. #19128753 | C22 | semidirect |
| 31. #19128753 | C22 | semidirect |
| 32. #19128753 | C22 | semidirect |
| 34. (C2×D167)⋊C8 | C22 | semidirect |
| 35. C4×C167⋊C8 | C22 | semidirect |
| 36. C2×D8×C167 | C22 | semidirect |
| 38. C4×D4×C167 | C22 | semidirect |
| 39. C4⋊C8×C167 | C22 | semidirect |
| 40. #102×C167 | C22 | semidirect |
| 85. D668 | D8 | semidirect |
| 86. D668 | #41 | semidirect |
| 142. C167 | #3294 | semidirect |
| 150. #459 | D167 | semidirect |
| 159. C2×D8 | C2×D167 | semidirect |
| 171. C4×D4 | C2×D167 | semidirect |
| 175. C4⋊C8 | C2×D167 | semidirect |
| 181. #102 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923924 | 2 |
| #24923904 | 2 |
| #24923615 | 2 |
| #24923581 | 2 |
| #24923550 | 2 |
| #24923502 | 2 |
| #24923401 | 2 |
| C4×#14581935 | 2 |
| #24923334 | 2 |
| #102×D167 | 2 |
| #459×C167 | 2 |
| #3294 | 167 |