Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
732 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 165 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×#15690835 | C2 | semidirect |
| 2. C22×#13095498 | C2 | semidirect |
| 3. #20261299 | C2 | semidirect |
| 4. #20260880 | C2 | semidirect |
| 5. #20260874 | C2 | semidirect |
| 6. #20260744 | C2 | semidirect |
| 7. #20260731 | C2 | semidirect |
| 8. #20260702 | C2 | semidirect |
| 9. C2×2−1+4×C97 | C2 | semidirect |
| 23. #15690734 | C22 | semidirect |
| 24. #15690734 | C22 | semidirect |
| 25. #15690731 | C22 | semidirect |
| 26. C22⋊#11715895 | C22 | semidirect |
| 33. C2×#41×C97 | C22 | semidirect |
| 36. C22×Q8×C97 | C22 | semidirect |
| 61. #41×C97 | D4 | semidirect |
| 69. C2×Q8×C97 | D4 | semidirect |
| 146. C97 | #3010 | semidirect |
| 147. C2×2−1+4 | D97 | semidirect |
| 162. C2×#41 | C2×D97 | semidirect |
| 165. C22×Q8 | C2×D97 | semidirect |
| 191. #41 | C22⋊D97 | semidirect |
| 199. C2×Q8 | C22⋊D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690835 | 2 |
| C22×#13095498 | 2 |
| #20261299 | 2 |
| #20260880 | 2 |
| #20260874 | 2 |
| #20260744 | 2 |
| #20260731 | 2 |
| #20260702 | 2 |
| C2×2−1+4×C97 | 2 |
| #3010 | 97 |