Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 11. #15690808 | C4 | semidirect |
| 101. C97 | #2327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690808 | 2 |
| C2×C4×Dic194 | 2 |
| #20260642 | 2 |
| #20260640 | 2 |
| #20260619 | 2 |
| #20260616 | 2 |
| #20260600 | 2 |
| #20260581 | 2 |
| C2×C4×Q8×C97 | 2 |
| #2327 | 97 |