Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
380 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 173 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. #20261144 | C2 | semidirect |
| 4. #20261140 | C2 | semidirect |
| 5. #20261133 | C2 | semidirect |
| 50. M16×C97 | Q8 | semidirect |
| 74. C8×C97 | C2×Q8 | semidirect |
| 93. C97 | #3165 | semidirect |
| 131. M16 | Dic194 | semidirect |
| 167. C8 | C2×Dic194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261292 | 2 |
| C2×#15690810 | 2 |
| #20261144 | 2 |
| #20261140 | 2 |
| #20261133 | 2 |
| #20260777 | 2 |
| C4×M16×C97 | 2 |
| #3165 | 97 |