Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 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×#15690840 | C2 | semidirect |
| 2. C2×#15690797 | C2 | semidirect |
| 3. #41×Dic97 | C2 | semidirect |
| 4. #20260955 | C2 | semidirect |
| 5. #20260948 | C2 | semidirect |
| 6. #20260758 | C2 | semidirect |
| 7. #20260745 | C2 | semidirect |
| 8. #20260740 | C2 | semidirect |
| 12. C2×#13095501 | C22 | semidirect |
| 13. C2×#13095499 | C22 | semidirect |
| 18. Q8×Dic97 | C22 | semidirect |
| 20. D4×Dic97 | C22 | semidirect |
| 26. #15690739 | C22 | semidirect |
| 27. #15690735 | C22 | semidirect |
| 126. C97 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690840 | 2 |
| C2×#15690797 | 2 |
| #41×Dic97 | 2 |
| #20260955 | 2 |
| #20260948 | 2 |
| #20260758 | 2 |
| #20260745 | 2 |
| #20260740 | 2 |
| C2×AGL(1,ℤ/8)×C97 | 2 |
| #3040 | 97 |