Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
340 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 113 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×#15690744 | C2 | semidirect |
| 2. C2×#15690734 | C2 | semidirect |
| 4. C2×#15690720 | C2 | semidirect |
| 5. #20260642 | C2 | semidirect |
| 22. C2×SD16×C97 | C4 | semidirect |
| 86. C8×C97 | C22⋊C4 | semidirect |
| 113. C97 | #1973 | semidirect |
| 125. C2×SD16 | Dic97 | semidirect |
| 200. C8 | C22⋊Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690744 | 2 |
| C2×#15690734 | 2 |
| C2×#15690731 | 2 |
| C2×#15690720 | 2 |
| #20260642 | 2 |
| #20260638 | 2 |
| C22×SD16×C97 | 2 |
| #1973 | 97 |