Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
458 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 458 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. C2×C4⋊C4×D167 | C2 | semidirect |
| 3. #24923603 | C2 | semidirect |
| 4. #24923598 | C2 | semidirect |
| 5. #24923586 | C2 | semidirect |
| 6. #24923581 | C2 | semidirect |
| 7. #24923311 | C2 | semidirect |
| 8. #24923309 | C2 | semidirect |
| 9. #24923270 | C2 | semidirect |
| 10. #24923232 | C2 | semidirect |
| 11. #417×C167 | C2 | semidirect |
| 30. #19128766 | C22 | semidirect |
| 31. #19128765 | C22 | semidirect |
| 32. #19128764 | C22 | semidirect |
| 33. #19128763 | C22 | semidirect |
| 34. #19128756 | C22 | semidirect |
| 35. #19128753 | C22 | semidirect |
| 41. #103×C167 | C22 | semidirect |
| 42. #102×C167 | C22 | semidirect |
| 155. C167 | #3092 | semidirect |
| 166. #417 | D167 | semidirect |
| 194. #103 | C2×D167 | semidirect |
| 196. #102 | C2×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923776 | 2 |
| C2×C4⋊C4×D167 | 2 |
| #24923603 | 2 |
| #24923598 | 2 |
| #24923586 | 2 |
| #24923581 | 2 |
| #24923311 | 2 |
| #24923309 | 2 |
| #24923270 | 2 |
| #24923232 | 2 |
| #417×C167 | 2 |
| #3092 | 167 |