Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
158 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 73. C97 | #2102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260783 | 2 |
| #20260758 | 2 |
| #20260507 | 2 |
| #20260496 | 2 |
| #20260494 | 2 |
| #20260491 | 2 |
| #344×C97 | 2 |
| #2102 | 97 |