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 |
|---|---|---|
| 2. #20261042 | C2 | direct (N × H) |
| 91. C2×C97 | #479 | semidirect |
| 96. C97 | C2×#479 | semidirect |
| 187. C2 | #20261042 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690802 | 2 |
| #20261042 | 2 |
| C2×#15690743 | 2 |
| C2×#15690741 | 2 |
| C2×C4⋊#11715895 | 2 |
| C2×#15690734 | 2 |
| C2×C4×Q8×C97 | 2 |
| C2×#479 | 97 |