Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
832 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 209 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×C4×C22⋊D97 | C2 | semidirect |
| 3. C2×#15690770 | C2 | semidirect |
| 4. #20260635 | C2 | semidirect |
| 5. #20260635 | C2 | semidirect |
| 6. #20260615 | C2 | semidirect |
| 7. #20260613 | C2 | semidirect |
| 8. #20260586 | C2 | semidirect |
| 9. #386×C97 | C2 | semidirect |
| 15. #15690806 | C4 | semidirect |
| 37. C2×D388 | C2×C4 | semidirect |
| 42. C2×C22⋊D97 | C2×C4 | semidirect |
| 43. C2×C22⋊D97 | C2×C4 | semidirect |
| 53. #13095490 | D4 | semidirect |
| 61. C4×Dic97 | C2×C4 | semidirect |
| 66. C2×D4×C97 | C2×C4 | semidirect |
| 144. Dic97 | C4×D4 | semidirect |
| 154. C97 | #2366 | semidirect |
| 162. #386 | D97 | semidirect |
| 202. C2×D4 | C4×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690806 | 2 |
| C2×C4×C22⋊D97 | 2 |
| C2×#15690770 | 2 |
| #20260635 | 2 |
| #20260615 | 2 |
| #20260613 | 2 |
| #20260586 | 2 |
| #386×C97 | 2 |
| #2366 | 97 |