Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
340 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 165 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. #20261144 | C2 | semidirect |
| 3. #20261140 | C2 | semidirect |
| 4. #20261137 | C2 | semidirect |
| 40. M16×C97 | Q8 | semidirect |
| 41. C2×C8×C97 | Q8 | semidirect |
| 81. C97 | #3164 | semidirect |
| 112. M16 | Dic194 | semidirect |
| 113. 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 |
| #20261144 | 2 |
| #20261140 | 2 |
| #20261137 | 2 |
| #20260777 | 2 |
| #20260773 | 2 |
| C2×#15690744 | 2 |
| #405×C97 | 2 |
| #3164 | 97 |