Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
872 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 233 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×#15690775 | C2 | semidirect |
| 3. #20260636 | C2 | semidirect |
| 4. #20260635 | C2 | semidirect |
| 5. #20260594 | C2 | semidirect |
| 6. C4×C22⋊Dic97 | C2 | semidirect |
| 7. #20260582 | C2 | semidirect |
| 8. #380×C97 | C2 | semidirect |
| 10. C2×#13095511 | C4 | semidirect |
| 82. C2×Dic97 | #41 | semidirect |
| 85. Dic194 | C22⋊C4 | semidirect |
| 115. C97 | #2341 | semidirect |
| 121. #380 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095511 | 2 |
| C2×#15690775 | 2 |
| #20260636 | 2 |
| #20260635 | 2 |
| #20260594 | 2 |
| C4×C22⋊Dic97 | 2 |
| #20260582 | 2 |
| #380×C97 | 2 |
| #2341 | 97 |