Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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. #20261212 | C2 | semidirect |
| 4. #20260837 | C2 | semidirect |
| 5. C4×#13095500 | C2 | semidirect |
| 6. #20260773 | C2 | semidirect |
| 7. #20260745 | C2 | semidirect |
| 9. #405×C97 | C2 | semidirect |
| 12. C2×#13095500 | C4 | semidirect |
| 15. C4×Dic194 | C22 | semidirect |
| 23. #15690744 | C22 | semidirect |
| 24. #15690742 | C22 | semidirect |
| 25. #15690735 | C22 | semidirect |
| 30. #97×C97 | C22 | semidirect |
| 31. C4×C8×C97 | C22 | semidirect |
| 35. C2×Dic194 | C2×C4 | semidirect |
| 43. #13095500 | C2×C4 | semidirect |
| 44. #13095500 | C2×C4 | semidirect |
| 56. C2×C8×C97 | C2×C4 | semidirect |
| 104. C97 | #2949 | semidirect |
| 113. #405 | D97 | semidirect |
| 134. #97 | C2×D97 | semidirect |
| 135. C4×C8 | C2×D97 | semidirect |
| 151. C2×C8 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095500 | 2 |
| #20261212 | 2 |
| #20261209 | 2 |
| #20260837 | 2 |
| C4×#13095500 | 2 |
| #20260773 | 2 |
| #20260745 | 2 |
| #20260741 | 2 |
| #405×C97 | 2 |
| #2949 | 97 |