Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
222 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20260792 | C2 | semidirect |
| 3. #20260471 | C2 | semidirect |
| 5. #382×C97 | C2 | semidirect |
| 7. #15690802 | C4 | semidirect |
| 8. #15690798 | C4 | semidirect |
| 12. C4×Dic194 | C4 | semidirect |
| 13. C4×D388 | C4 | semidirect |
| 98. C97 | #1512 | semidirect |
| 101. #382 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261269 | 2 |
| #20260792 | 2 |
| #20260471 | 2 |
| #20260468 | 2 |
| #382×C97 | 2 |
| #1512 | 97 |