Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
348 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 3. #20261143 | C2 | semidirect |
| 4. #20261142 | C2 | semidirect |
| 5. #20261136 | C2 | semidirect |
| 6. #20261135 | C2 | semidirect |
| 48. #13095495 | Q8 | semidirect |
| 72. M16×C97 | Q8 | semidirect |
| 125. C97 | #3166 | semidirect |
| 176. M16 | Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261288 | 2 |
| C2×#15690801 | 2 |
| #20261143 | 2 |
| #20261142 | 2 |
| #20261136 | 2 |
| #20261135 | 2 |
| #20260778 | 2 |
| #20260777 | 2 |
| #20260775 | 2 |
| M16×Dic97 | 2 |
| #428×C97 | 2 |
| #3166 | 97 |