Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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. #20260782 | C2 | semidirect |
| 3. #20260557 | C2 | semidirect |
| 4. #20260549 | C2 | semidirect |
| 5. #20260547 | C2 | semidirect |
| 6. #20260516 | C2 | semidirect |
| 7. #365×C97 | C2 | semidirect |
| 66. C97 | #2238 | semidirect |
| 70. #365 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260989 | 2 |
| #20260782 | 2 |
| #20260557 | 2 |
| #20260549 | 2 |
| #20260547 | 2 |
| #20260516 | 2 |
| #365×C97 | 2 |
| #2238 | 97 |