Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 3. #20261142 | C2 | direct (N × H) |
| 35. C2×#11715895 | Q8 | semidirect |
| 49. C2×C8×C97 | Q8 | semidirect |
| 73. C8×C97 | C2×Q8 | semidirect |
| 74. #11715895 | C2×Q8 | semidirect |
| 88. C2×C97 | #501 | semidirect |
| 93. C97 | C2×#501 | semidirect |
| 133. C2×C8 | Dic194 | semidirect |
| 167. C8 | C2×Dic194 | semidirect |
| 181. C2 | #20261142 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690809 | 2 |
| C2×#15690801 | 2 |
| #20261142 | 2 |
| C2×#15690744 | 2 |
| C2×#15690743 | 2 |
| C2×#15690741 | 2 |
| C2×#15690720 | 2 |
| C2×#106×C97 | 2 |
| C2×#501 | 97 |