Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
576 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 242 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. #20261738 | C2 | direct (N × H) |
| 3. C2×#15690877 | C2 | semidirect |
| 4. C2×C4⋊#11715897 | C2 | semidirect |
| 9. #15690877 | C22 | semidirect |
| 10. C4⋊#11715897 | C22 | semidirect |
| 51. C2×C4×C97 | M16 | semidirect |
| 58. C2×Dic97 | M16 | semidirect |
| 78. C4×C97 | C2×M16 | semidirect |
| 82. Dic97 | C2×M16 | semidirect |
| 86. C2×C97 | #423 | semidirect |
| 91. C97 | C2×#423 | semidirect |
| 156. C2×C4 | #13095520 | semidirect |
| 175. C4 | C2×#13095520 | semidirect |
| 177. C2 | #20261738 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095520 | 2 |
| #20261738 | 2 |
| C2×#15690877 | 2 |
| C2×C4⋊#11715897 | 2 |
| C22×C4×Dic97 | 2 |
| C2×#423 | 97 |