Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20260759 | C2 | semidirect |
| 2. C2×#15690737 | C2 | semidirect |
| 3. C42×Dic97 | C2 | semidirect |
| 11. C4⋊Q8×C97 | C4 | semidirect |
| 12. #127×C97 | C4 | semidirect |
| 13. #124×C97 | C4 | semidirect |
| 22. C4×Dic97 | D4 | semidirect |
| 63. C4×C97 | #104 | semidirect |
| 73. C97 | #1962 | semidirect |
| 80. C4⋊Q8 | Dic97 | semidirect |
| 81. #127 | Dic97 | semidirect |
| 82. #124 | Dic97 | semidirect |
| 137. C4 | #15690737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260759 | 2 |
| C2×#15690737 | 2 |
| C42×Dic97 | 2 |
| #532×C97 | 2 |
| #1962 | 97 |