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×C13×C22⋊Q8 | C2 | semidirect |
| 3. C2×#88201 | C2 | semidirect |
| 4. C4×C22⋊Dic13 | C2 | semidirect |
| 5. #11718652 | C2 | semidirect |
| 6. #11718649 | C2 | semidirect |
| 7. #11718616 | C2 | semidirect |
| 9. C22×Q8×C13 | C22 | semidirect |
| 16. C2×C13×C4⋊C4 | C22 | semidirect |
| 17. C2×C13×C4⋊C4 | C22 | semidirect |
| 21. C2×#6103 | C22 | semidirect |
| 22. C2×#6103 | C22 | semidirect |
| 23. C2×C4×Dic13 | C22 | semidirect |
| 24. #88071 | C22 | semidirect |
| 85. C2×C22⋊Q8 | D13 | semidirect |
| 93. C22×C13 | #124 | semidirect |
| 110. C22×Q8 | C2×D13 | semidirect |
| 118. C2×C4⋊C4 | C2×D13 | semidirect |
| 119. C2×C4⋊C4 | C2×D13 | semidirect |
| 160. C13 | #2435 | semidirect |
| 199. C22 | #88201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D52 | 2 |
| C2×C13×C22⋊Q8 | 2 |
| C2×#88201 | 2 |
| C4×C22⋊Dic13 | 2 |
| #11718652 | 2 |
| #11718649 | 2 |
| #11718616 | 2 |
| #2435 | 13 |