Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
266 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20260758 | C2 | semidirect |
| 3. C2×#15690737 | C2 | semidirect |
| 4. C2×#15690736 | C2 | semidirect |
| 5. #20260717 | C2 | semidirect |
| 6. #20260493 | C2 | semidirect |
| 7. #413×C97 | C2 | semidirect |
| 123. C97 | #2050 | semidirect |
| 129. #413 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261533 | 2 |
| #20260758 | 2 |
| C2×#15690737 | 2 |
| C2×#15690736 | 2 |
| #20260717 | 2 |
| #20260493 | 2 |
| #413×C97 | 2 |
| #2050 | 97 |