Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 1. C2×#15690840 | C2 | semidirect |
| 2. C2×C4×Dic194 | C2 | semidirect |
| 3. #20260954 | C2 | semidirect |
| 4. #20260942 | C2 | semidirect |
| 5. #20260932 | C2 | semidirect |
| 6. #20260759 | C2 | semidirect |
| 7. #20260736 | C2 | semidirect |
| 36. C2×Dic194 | D4 | semidirect |
| 110. C4×C97 | #137 | semidirect |
| 121. C97 | #3037 | semidirect |
| 233. C4 | #15690840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690840 | 2 |
| C2×C4×Dic194 | 2 |
| #20260954 | 2 |
| #20260942 | 2 |
| #20260932 | 2 |
| #20260759 | 2 |
| #20260736 | 2 |
| #532×C97 | 2 |
| #3037 | 97 |