Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 87 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×#15690732 | C2 | semidirect |
| 3. C2×#15690731 | C2 | semidirect |
| 4. C2×#15690730 | C2 | semidirect |
| 5. #20260631 | C2 | semidirect |
| 6. #20260489 | C2 | semidirect |
| 7. C2×#102×C97 | C2 | semidirect |
| 45. C4⋊Dic97 | D4 | semidirect |
| 147. C97 | #2041 | semidirect |
| 152. C2×#102 | 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×#15690732 | 2 |
| C2×#15690731 | 2 |
| C2×#15690730 | 2 |
| #20260631 | 2 |
| #20260489 | 2 |
| C2×#102×C97 | 2 |
| #2041 | 97 |