Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
576 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 234 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. #20261740 | C2 | direct (N × H) |
| 3. C2×#15690877 | C2 | semidirect |
| 8. #15690877 | C22 | semidirect |
| 42. C2×Dic97 | M16 | semidirect |
| 62. Dic97 | C2×M16 | semidirect |
| 65. C2×C97 | #423 | semidirect |
| 70. C97 | C2×#423 | semidirect |
| 136. C2 | #20261740 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095521 | 2 |
| #20261740 | 2 |
| C2×#15690877 | 2 |
| C2×C42×D97 | 2 |
| C2×#423 | 97 |