Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
488 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 6. #11718534 | C2 | direct (N × H) |
| 14. C2×Dic52 | C4 | semidirect |
| 40. Dic52 | C2×C4 | semidirect |
| 52. C2×Dic13 | Q16 | semidirect |
| 76. Dic13 | C2×Q16 | semidirect |
| 91. C2×C13 | C4×Q16 | semidirect |
| 115. C13 | C2×C4×Q16 | semidirect |
| 145. C2 | #11718534 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic52 | 2 |
| C2×#88141 | 2 |
| C2×C13×#107 | 2 |
| C2×C8×Dic13 | 2 |
| C2×#88050 | 2 |
| #11718534 | 2 |
| C2×C4×Q16 | 13 |