Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 97 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×#15690736 | C2 | semidirect |
| 3. C42×Dic97 | C2 | semidirect |
| 4. #423×C97 | C2 | semidirect |
| 6. #15690810 | C4 | semidirect |
| 7. #15690807 | C4 | semidirect |
| 8. #15690798 | C4 | semidirect |
| 29. C4×Dic97 | D4 | semidirect |
| 62. C4×C97 | #104 | semidirect |
| 73. C97 | #1962 | semidirect |
| 75. #423 | D97 | semidirect |
| 137. C4 | #15690736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261285 | 2 |
| C2×#15690736 | 2 |
| C42×Dic97 | 2 |
| #423×C97 | 2 |
| #1962 | 97 |