Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. #11719284 | C2 | semidirect |
| 2. Q8×D52 | C2 | semidirect |
| 3. C13×#446 | C2 | semidirect |
| 4. #11718508 | C2 | semidirect |
| 5. #11718507 | C2 | semidirect |
| 6. #11718503 | C2 | semidirect |
| 7. #11718503 | C2 | semidirect |
| 9. #11718363 | C2 | semidirect |
| 11. #11718341 | C2 | semidirect |
| 72. D104 | Q8 | semidirect |
| 89. D52 | C2×Q8 | semidirect |
| 99. C8×C13 | C2×Q8 | semidirect |
| 108. #446 | D13 | semidirect |
| 194. C13 | #3384 | semidirect |
| 220. C8 | Q8×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719284 | 2 |
| Q8×D52 | 2 |
| C13×#446 | 2 |
| #11718508 | 2 |
| #11718507 | 2 |
| #11718503 | 2 |
| #11718372 | 2 |
| #11718363 | 2 |
| C4×D104 | 2 |
| #11718341 | 2 |
| #3384 | 13 |