Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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. C13×#500 | C2 | semidirect |
| 4. #11718740 | C2 | semidirect |
| 5. #11718739 | C2 | semidirect |
| 7. #11718537 | C2 | semidirect |
| 9. #11718341 | C2 | semidirect |
| 65. #6094 | Q8 | semidirect |
| 87. C8×C13 | C2×Q8 | semidirect |
| 88. #1055 | C2×Q8 | semidirect |
| 93. #500 | D13 | semidirect |
| 172. C13 | #3165 | semidirect |
| 194. C8 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719433 | 2 |
| D13×C4⋊Q8 | 2 |
| C13×#500 | 2 |
| #11718740 | 2 |
| #11718739 | 2 |
| #11718542 | 2 |
| #11718537 | 2 |
| C4×#6094 | 2 |
| #11718341 | 2 |
| #3165 | 13 |