Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
488 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 221 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. C4×#13095501 | C2 | direct (N × H) |
| 10. C2×#13095501 | C4 | direct (N × H) |
| 36. #13095501 | C2×C4 | direct (N × H) |
| 69. C2×C4×C97 | Q16 | semidirect |
| 93. C4×C97 | C2×Q16 | semidirect |
| 98. C2×C97 | C4×Q16 | semidirect |
| 103. C97 | C2×C4×Q16 | semidirect |
| 179. C2×C4 | #13095501 | direct (N × H) |
| 198. C4 | C2×#13095501 | direct (N × H) |
| 201. C2 | C4×#13095501 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095501 | 2 |
| C2×C4×Dic194 | 2 |
| C4×#13095501 | 2 |
| C2×#15690743 | 2 |
| C2×#15690734 | 2 |
| C2×#15690733 | 2 |
| C2×C4×#11715895 | 2 |
| C2×C4×Q8×C97 | 2 |
| C2×C4×Q16 | 97 |