Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
320 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 320 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 |
|---|---|---|
| 3. #20260581 | C2 | semidirect |
| 4. #20260496 | C2 | semidirect |
| 5. C4×M16×C97 | C2 | semidirect |
| 7. C4×Dic194 | C4 | semidirect |
| 8. C4×D388 | C4 | semidirect |
| 14. #15690736 | C4 | semidirect |
| 35. C4×Dic97 | C2×C4 | semidirect |
| 39. M16×C97 | C2×C4 | semidirect |
| 83. C97 | #1759 | semidirect |
| 86. C4×M16 | D97 | semidirect |
| 114. M16 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13095511 | 2 |
| C2×#15690736 | 2 |
| #20260581 | 2 |
| #20260496 | 2 |
| C4×M16×C97 | 2 |
| #1759 | 97 |