Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
544 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 3. C2×#88123 | C2 | semidirect |
| 4. C2×C13×C4⋊C8 | C2 | semidirect |
| 5. C2×#88056 | C2 | semidirect |
| 6. #11718502 | C2 | direct (N × H) |
| 21. #88123 | C22 | semidirect |
| 22. C13×C4⋊C8 | C22 | semidirect |
| 23. #88056 | C22 | semidirect |
| 57. C2×C4×C13 | SD16 | semidirect |
| 80. C2×C4⋊C8 | D13 | semidirect |
| 92. C4×C13 | C2×SD16 | semidirect |
| 112. C4⋊C8 | C2×D13 | semidirect |
| 114. C2×C13 | #461 | semidirect |
| 145. C13 | C2×#461 | semidirect |
| 163. C2×C4 | #6095 | semidirect |
| 183. C4 | C2×#6095 | semidirect |
| 187. C2 | #11718502 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6095 | 2 |
| C2×C4×D52 | 2 |
| C2×#88123 | 2 |
| C2×C13×C4⋊C8 | 2 |
| C2×#88056 | 2 |
| #11718502 | 2 |
| C2×#461 | 13 |