Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×#15690897 | C2 | semidirect |
| 2. C2×#15690874 | C2 | semidirect |
| 3. C2×#15690874 | C2 | semidirect |
| 4. #20261709 | C2 | semidirect |
| 5. #20261611 | C2 | semidirect |
| 6. #20261600 | C2 | semidirect |
| 24. C2×Dic388 | C4 | semidirect |
| 25. C2×#13095499 | C4 | semidirect |
| 26. C2×#13095499 | C4 | semidirect |
| 28. C2×D8×C97 | C4 | semidirect |
| 131. C97 | #1876 | semidirect |
| 146. C2×D8 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690897 | 2 |
| C2×#15690874 | 2 |
| #20261709 | 2 |
| #20261611 | 2 |
| #20261600 | 2 |
| C2×#15690829 | 2 |
| #1876 | 97 |