Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #20260691 | C2 | semidirect |
| 4. C2×#15690720 | C2 | semidirect |
| 5. #20260500 | C2 | semidirect |
| 6. #20260494 | C2 | semidirect |
| 9. #15690817 | C4 | semidirect |
| 16. #15690737 | C4 | semidirect |
| 23. #103×C97 | C4 | semidirect |
| 24. #102×C97 | C4 | semidirect |
| 99. C97 | #1765 | semidirect |
| 119. #103 | Dic97 | semidirect |
| 120. #102 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690817 | 2 |
| C2×#15690737 | 2 |
| #20260691 | 2 |
| C2×#15690720 | 2 |
| #20260500 | 2 |
| #20260494 | 2 |
| #416×C97 | 2 |
| #1765 | 97 |