Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
400 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 186 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 |
|---|---|---|
| 1. #20261787 | C2 | direct (N × H) |
| 31. C2×#11715897 | Q8 | semidirect |
| 75. #11715897 | C2×Q8 | semidirect |
| 89. C2×C97 | #446 | semidirect |
| 94. C97 | C2×#446 | semidirect |
| 183. C2 | #20261787 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261787 | 2 |
| C2×#15690877 | 2 |
| C2×C4⋊#11715897 | 2 |
| C2×#15690865 | 2 |
| C2×C4×#11715897 | 2 |
| C2×#15690775 | 2 |
| C2×#446 | 97 |