Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
476 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 293 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. #20260777 | C2 | semidirect |
| 3. #20260773 | C2 | semidirect |
| 4. C2×#15690744 | C2 | semidirect |
| 15. #131×C97 | C4 | semidirect |
| 29. M16×C97 | C2×C4 | semidirect |
| 30. C2×C8×C97 | C2×C4 | semidirect |
| 59. C97 | #2913 | semidirect |
| 66. #131 | Dic97 | semidirect |
| 83. M16 | C2×Dic97 | semidirect |
| 84. C2×C8 | C2×Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261218 | 2 |
| #20260777 | 2 |
| #20260773 | 2 |
| C2×#15690744 | 2 |
| C2×#131×C97 | 2 |
| #2913 | 97 |