Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
284 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 68 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. C2×#15690864 | C2 | semidirect |
| 4. #20261686 | C2 | semidirect |
| 5. #20261609 | C2 | semidirect |
| 6. #20261608 | C2 | semidirect |
| 21. #15690732 | C4 | semidirect |
| 22. #15690731 | C4 | semidirect |
| 23. #15690730 | C4 | semidirect |
| 24. #102×C97 | C4 | semidirect |
| 135. C97 | #1936 | semidirect |
| 157. #102 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690872 | 2 |
| C2×#15690864 | 2 |
| #20261687 | 2 |
| #20261686 | 2 |
| #20261609 | 2 |
| #20261608 | 2 |
| #102×D97 | 2 |
| #1936 | 97 |