Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 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. #20261750 | C2 | semidirect |
| 4. M16×#87604 | C2 | semidirect |
| 5. #20261618 | C2 | semidirect |
| 6. #20261607 | C2 | semidirect |
| 23. #15690728 | C4 | semidirect |
| 24. #15690728 | C4 | semidirect |
| 25. #15690727 | C4 | semidirect |
| 26. #100×C97 | C4 | semidirect |
| 106. C97 | #1932 | semidirect |
| 130. #100 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261750 | 2 |
| #20261733 | 2 |
| C2×#15690874 | 2 |
| M16×#87604 | 2 |
| #20261618 | 2 |
| #20261607 | 2 |
| #20260716 | 2 |
| #1932 | 97 |