Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×Dic194 | C2 | semidirect |
| 2. C2×#15690840 | C2 | semidirect |
| 3. #20260890 | C2 | semidirect |
| 4. #20260873 | C2 | semidirect |
| 5. #20260743 | C2 | semidirect |
| 6. #20260699 | C2 | semidirect |
| 15. C2×#13095501 | C22 | semidirect |
| 16. C2×#13095499 | C22 | semidirect |
| 18. #15690733 | C22 | semidirect |
| 34. C2×Dic194 | D4 | semidirect |
| 95. C22×C97 | #137 | semidirect |
| 109. C97 | #3004 | semidirect |
| 204. C22 | #15690840 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic194 | 2 |
| C2×#15690840 | 2 |
| #20260890 | 2 |
| #20260873 | 2 |
| #20260743 | 2 |
| #20260699 | 2 |
| #525×C97 | 2 |
| #3004 | 97 |