Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
336 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#15690738 | C2 | semidirect |
| 3. C4×#13095495 | C2 | semidirect |
| 4. C4×C4⋊C4×C97 | C2 | semidirect |
| 7. #15690810 | C4 | semidirect |
| 8. #15690807 | C4 | semidirect |
| 9. #15690798 | C4 | semidirect |
| 30. #13095495 | D4 | semidirect |
| 82. C4×C97 | #104 | semidirect |
| 93. C97 | #1980 | semidirect |
| 97. C4×C4⋊C4 | D97 | semidirect |
| 176. C4 | #15690738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261285 | 2 |
| C2×#15690738 | 2 |
| C4×#13095495 | 2 |
| C4×C4⋊C4×C97 | 2 |
| #1980 | 97 |