Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 91. Dic194 | Q16 | semidirect |
| 113. C97 | #3363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261465 | 2 |
| #20261460 | 2 |
| #20261084 | 2 |
| #20261028 | 2 |
| #20261027 | 2 |
| #20260944 | 2 |
| #20260942 | 2 |
| C8×Dic194 | 2 |
| C4×Dic388 | 2 |
| #20260827 | 2 |
| #487×C97 | 2 |
| #3363 | 97 |