Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
264 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 1. #20260788 | C2 | semidirect |
| 2. #20260461 | C2 | semidirect |
| 22. C22×C4×C97 | C8 | semidirect |
| 85. C97 | #1458 | semidirect |
| 106. C22×C4 | #11715895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260788 | 2 |
| #20260461 | 2 |
| #20260459 | 2 |
| C2×#117×C97 | 2 |
| #1458 | 97 |