Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
362 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11719226 | C2 | semidirect |
| 3. #11718800 | C2 | semidirect |
| 4. C2×#88063 | C2 | semidirect |
| 5. #11718666 | C2 | semidirect |
| 6. C13×H(3,ℤ/4) | C2 | semidirect |
| 7. #11718123 | C2 | semidirect |
| 19. #88129 | C4 | semidirect |
| 20. #88128 | C4 | semidirect |
| 38. C2×D52 | C2×C4 | semidirect |
| 42. C2×Dic26 | C2×C4 | semidirect |
| 50. C42×C13 | C2×C4 | semidirect |
| 51. C42×C13 | D4 | semidirect |
| 56. C4×Dic13 | D4 | semidirect |
| 99. H(3,ℤ/4) | D13 | semidirect |
| 174. C42 | C4×D13 | semidirect |
| 175. C42 | D52 | semidirect |
| 176. C13 | #1911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719230 | 2 |
| #11719226 | 2 |
| #11718800 | 2 |
| C2×#88063 | 2 |
| #11718666 | 2 |
| C13×H(3,ℤ/4) | 2 |
| #11718123 | 2 |
| #1911 | 13 |