Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19128838 | C2 | semidirect |
| 2. #24923843 | C2 | semidirect |
| 4. #24923512 | C2 | semidirect |
| 5. #24923495 | C2 | semidirect |
| 6. #24923307 | C2 | semidirect |
| 7. #24923278 | C2 | semidirect |
| 8. #24923274 | C2 | semidirect |
| 9. C22×SD16×C167 | C2 | semidirect |
| 13. C2×#14581933 | C22 | semidirect |
| 14. C2×C8×D167 | C22 | semidirect |
| 20. #19128808 | C22 | semidirect |
| 25. #19128766 | C22 | semidirect |
| 26. #19128764 | C22 | semidirect |
| 27. #19128756 | C22 | semidirect |
| 68. C2×C8×C167 | D4 | semidirect |
| 120. C167 | #3057 | semidirect |
| 122. C22×SD16 | D167 | semidirect |
| 180. C2×C8 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128838 | 2 |
| #24923843 | 2 |
| #24923836 | 2 |
| #24923512 | 2 |
| #24923495 | 2 |
| #24923307 | 2 |
| #24923278 | 2 |
| #24923274 | 2 |
| C22×SD16×C167 | 2 |
| #3057 | 167 |