Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1088 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 181 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. C2×#88178 | C2 | semidirect |
| 3. C2×#88129 | C2 | semidirect |
| 4. C4×C13×C22⋊C4 | C2 | semidirect |
| 5. #11718616 | C2 | semidirect |
| 6. #11718600 | C2 | semidirect |
| 7. #11718333 | C2 | semidirect |
| 14. C22×Dic26 | C22 | semidirect |
| 16. C2×C42×C13 | C22 | semidirect |
| 18. C2×#6103 | C22 | semidirect |
| 19. C2×#6103 | C22 | semidirect |
| 20. C2×C4⋊Dic13 | C22 | semidirect |
| 22. C2×#6101 | C22 | semidirect |
| 24. C13×#95 | C22 | semidirect |
| 89. C4×C22⋊C4 | D13 | semidirect |
| 93. C22×C13 | #124 | semidirect |
| 124. C2×C42 | C2×D13 | semidirect |
| 125. #95 | C2×D13 | semidirect |
| 160. C13 | #2435 | semidirect |
| 199. C22 | #88129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D52 | 2 |
| C2×#88178 | 2 |
| C2×#88129 | 2 |
| C4×C13×C22⋊C4 | 2 |
| #11718616 | 2 |
| #11718600 | 2 |
| #11718333 | 2 |
| #2435 | 13 |