Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
236 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 84. C97 | #1830 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261212 | 2 |
| C2×#15690728 | 2 |
| #20260507 | 2 |
| #20260506 | 2 |
| #20260505 | 2 |
| #344×C97 | 2 |
| #1830 | 97 |