Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
380 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 141 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×#501 | C2 | semidirect |
| 4. #11718741 | C2 | semidirect |
| 5. #11718726 | C2 | semidirect |
| 7. #11718535 | C2 | semidirect |
| 9. #11718516 | C2 | semidirect |
| 11. #11718363 | C2 | semidirect |
| 79. #6094 | Q8 | semidirect |
| 103. C8×C13 | C2×Q8 | semidirect |
| 104. #1055 | C2×Q8 | semidirect |
| 110. #501 | D13 | semidirect |
| 204. C13 | #3165 | semidirect |
| 228. C8 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×C4⋊Q8 | 2 |
| #11719393 | 2 |
| C13×#501 | 2 |
| #11718741 | 2 |
| #11718726 | 2 |
| #11718542 | 2 |
| #11718535 | 2 |
| #11718522 | 2 |
| #11718516 | 2 |
| #11718368 | 2 |
| #11718363 | 2 |
| #3165 | 13 |