Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
484 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 484 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. #20261216 | C2 | semidirect |
| 3. #20260834 | C2 | semidirect |
| 4. #20260829 | C2 | semidirect |
| 5. #20260817 | C2 | semidirect |
| 6. #20260734 | C2 | semidirect |
| 7. #20260690 | C2 | semidirect |
| 8. C2×#107×C97 | C2 | semidirect |
| 10. #15690832 | C4 | semidirect |
| 30. #13095511 | C2×C4 | semidirect |
| 36. Dic388 | C2×C4 | semidirect |
| 37. #13095500 | C2×C4 | semidirect |
| 38. D776 | C2×C4 | semidirect |
| 50. C2×C8×C97 | C2×C4 | semidirect |
| 96. C97 | #2951 | semidirect |
| 102. C2×#107 | D97 | semidirect |
| 139. 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 |
| #20261216 | 2 |
| #20260834 | 2 |
| #20260829 | 2 |
| #20260817 | 2 |
| #20260734 | 2 |
| #20260690 | 2 |
| C2×#107×C97 | 2 |
| #2951 | 97 |