Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 2. C2×#15690721 | C2 | semidirect |
| 3. #20260476 | C2 | semidirect |
| 4. #20260474 | C2 | semidirect |
| 5. C4×M16×C97 | C2 | semidirect |
| 92. C97 | #1524 | semidirect |
| 94. C4×M16 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261269 | 2 |
| C2×#15690721 | 2 |
| #20260476 | 2 |
| #20260474 | 2 |
| C4×M16×C97 | 2 |
| #1524 | 97 |