Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
340 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 149 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. #20261142 | C2 | semidirect |
| 3. #20261139 | C2 | semidirect |
| 4. #20261136 | C2 | semidirect |
| 30. #13095495 | Q8 | semidirect |
| 42. C2×C8×C97 | Q8 | semidirect |
| 81. C97 | #3164 | semidirect |
| 114. C2×C8 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261363 | 2 |
| #20261142 | 2 |
| #20261139 | 2 |
| #20261136 | 2 |
| #20260778 | 2 |
| C2×#15690744 | 2 |
| #20260690 | 2 |
| #427×C97 | 2 |
| #3164 | 97 |