Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1008 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 242 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. C22×#6118 | C2 | semidirect |
| 3. C2×C22⋊#1057 | C2 | semidirect |
| 4. #11719127 | C2 | direct (N × H) |
| 5. C2×#88111 | C2 | semidirect |
| 16. C22×#1057 | C22 | semidirect |
| 18. C2×#6118 | C22 | semidirect |
| 19. C22⋊#1057 | C22 | semidirect |
| 20. #88111 | C22 | semidirect |
| 50. C2×#1057 | C23 | semidirect |
| 55. C23×C13 | M16 | semidirect |
| 67. C22×D13 | M16 | semidirect |
| 100. C22×C13 | C2×M16 | semidirect |
| 110. C2×D13 | C2×M16 | semidirect |
| 132. C2×C13 | #407 | semidirect |
| 169. C13 | C2×#407 | semidirect |
| 184. C23 | #6118 | semidirect |
| 219. C22 | C2×#6118 | semidirect |
| 231. C2 | #11719127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D13 | 2 |
| C22×#6118 | 2 |
| C2×C22⋊#1057 | 2 |
| #11719127 | 2 |
| C2×#88111 | 2 |
| C2×#407 | 13 |