Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 230 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 |
|---|---|---|
| 1. C2×#15690729 | C2 | semidirect |
| 2. #20260534 | C2 | semidirect |
| 3. #20260532 | C2 | semidirect |
| 76. C97 | #2133 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690729 | 2 |
| #20260534 | 2 |
| #20260532 | 2 |
| #536×C97 | 2 |
| #2133 | 97 |