Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20260843 | C2 | semidirect |
| 3. #20260559 | C2 | semidirect |
| 4. #20260550 | C2 | semidirect |
| 6. #20260513 | C2 | semidirect |
| 10. #15690756 | C4 | semidirect |
| 11. #15690754 | C4 | semidirect |
| 65. C97 | #2180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261175 | 2 |
| #20260843 | 2 |
| #20260559 | 2 |
| #20260550 | 2 |
| #20260545 | 2 |
| #20260513 | 2 |
| #444×C97 | 2 |
| #2180 | 97 |