Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
224 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 93 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. C22×C13×C16 | C2 | semidirect |
| 3. C2×#88052 | C2 | semidirect |
| 4. #11718100 | C2 | direct (N × H) |
| 16. C2×C13×C16 | C22 | semidirect |
| 18. #88052 | C22 | semidirect |
| 69. C22×C16 | D13 | semidirect |
| 96. C2×C16 | C2×D13 | semidirect |
| 99. C2×C13 | #350 | semidirect |
| 126. C13 | C2×#350 | semidirect |
| 163. C2 | #11718100 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88155 | 2 |
| C22×C13×C16 | 2 |
| C2×#88052 | 2 |
| #11718100 | 2 |
| C2×#350 | 13 |