Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #20261203 | C2 | semidirect |
| 3. #20260846 | C2 | semidirect |
| 4. #20260841 | C2 | semidirect |
| 5. #20260834 | C2 | semidirect |
| 6. #20260729 | C2 | semidirect |
| 7. C2×#15690720 | C2 | semidirect |
| 8. #427×C97 | C2 | semidirect |
| 10. #15690832 | C4 | semidirect |
| 30. #13095511 | C2×C4 | semidirect |
| 37. Dic388 | C2×C4 | semidirect |
| 38. #13095500 | C2×C4 | semidirect |
| 39. D776 | C2×C4 | semidirect |
| 48. C2×C8×C97 | C2×C4 | semidirect |
| 90. C97 | #2943 | semidirect |
| 96. #427 | D97 | semidirect |
| 133. C2×C8 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| #20261203 | 2 |
| #20260846 | 2 |
| #20260841 | 2 |
| #20260834 | 2 |
| #20260729 | 2 |
| C2×#15690720 | 2 |
| #427×C97 | 2 |
| #2943 | 97 |