Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
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 |
|---|---|---|
| 8. #11719078 | C2 | direct (N × H) |
| 40. C2×#1057 | Q8 | semidirect |
| 76. #1057 | C2×Q8 | semidirect |
| 117. C2×C13 | #446 | semidirect |
| 147. C13 | C2×#446 | semidirect |
| 183. C2 | #11719078 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88141 | 2 |
| C2×#88112 | 2 |
| C2×#88110 | 2 |
| C2×C4⋊#1057 | 2 |
| C2×C4×#1057 | 2 |
| #11719078 | 2 |
| C2×#446 | 13 |