Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
312 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 80 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. C4×C4⋊#261 | C2 | semidirect |
| 4. #11719052 | C2 | semidirect |
| 5. #11718247 | C2 | semidirect |
| 10. C4×Q8×C13 | C4 | semidirect |
| 11. Q8×Dic13 | C4 | semidirect |
| 13. #88147 | C4 | semidirect |
| 17. C4×D52 | C4 | semidirect |
| 65. Q8×C13 | C4⋊C4 | semidirect |
| 78. D52 | C4⋊C4 | semidirect |
| 107. C4×C13 | #104 | semidirect |
| 118. C4×Q8 | #261 | semidirect |
| 173. C13 | #1806 | semidirect |
| 177. Q8 | C4⋊#261 | semidirect |
| 222. C4 | #88118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6131 | 2 |
| C2×#88118 | 2 |
| C4×C4⋊#261 | 2 |
| #11719052 | 2 |
| #11718247 | 2 |
| #1806 | 13 |