Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#15690858 | C2 | semidirect |
| 2. C2×#15690830 | C2 | semidirect |
| 3. #20261313 | C2 | semidirect |
| 4. #20260896 | C2 | semidirect |
| 5. #20260889 | C2 | semidirect |
| 6. #20260879 | C2 | semidirect |
| 7. #20260872 | C2 | semidirect |
| 8. #20260737 | C2 | semidirect |
| 9. C2×#15690734 | C2 | semidirect |
| 10. #20260703 | C2 | semidirect |
| 11. C2×#137×C97 | C2 | semidirect |
| 52. #13095511 | D4 | semidirect |
| 86. C2×Q8×C97 | D4 | semidirect |
| 170. C97 | #3013 | semidirect |
| 172. C2×#137 | D97 | semidirect |
| 233. 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×#15690858 | 2 |
| C2×#15690830 | 2 |
| #20261313 | 2 |
| #20260896 | 2 |
| #20260889 | 2 |
| #20260879 | 2 |
| #20260872 | 2 |
| #20260737 | 2 |
| C2×#15690734 | 2 |
| #20260703 | 2 |
| C2×#137×C97 | 2 |
| #3013 | 97 |