Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
752 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 309 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 |
|---|---|---|
| 3. #20260744 | C2 | direct (N × H) |
| 4. C2×#15690734 | C2 | semidirect |
| 14. #15690734 | C22 | semidirect |
| 18. C22×Q8×C97 | C4 | semidirect |
| 39. C2×Q8×C97 | C2×C4 | semidirect |
| 86. C2×C97 | #419 | semidirect |
| 90. C97 | C2×#419 | semidirect |
| 99. C22×Q8 | Dic97 | semidirect |
| 121. C2×Q8 | C2×Dic97 | semidirect |
| 176. C2 | #20260744 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095495 | 2 |
| C2×#15690769 | 2 |
| #20260744 | 2 |
| C2×#15690734 | 2 |
| C23×Q8×C97 | 2 |
| C2×#419 | 97 |