Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20261209 | C2 | semidirect |
| 3. #20260751 | C2 | semidirect |
| 4. #20260741 | C2 | semidirect |
| 5. #20260708 | C2 | semidirect |
| 6. #20260492 | C2 | semidirect |
| 7. #344×C97 | C2 | semidirect |
| 12. C2×#13095500 | C4 | semidirect |
| 13. C2×D776 | C4 | semidirect |
| 30. C2×Dic194 | C2×C4 | semidirect |
| 35. C2×D388 | C2×C4 | semidirect |
| 56. C2×C8×C97 | C2×C4 | semidirect |
| 116. C97 | #1904 | semidirect |
| 122. #344 | D97 | semidirect |
| 165. 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×#15690838 | 2 |
| #20261209 | 2 |
| #20260751 | 2 |
| #20260741 | 2 |
| #20260708 | 2 |
| #20260492 | 2 |
| #344×C97 | 2 |
| #1904 | 97 |