Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×#88116 | C2 | semidirect |
| 3. C4×C4⋊#261 | C2 | semidirect |
| 4. C4×#6118 | C2 | semidirect |
| 9. C13×#127 | C4 | semidirect |
| 12. #88190 | C4 | semidirect |
| 16. #88123 | C4 | semidirect |
| 37. #6118 | D4 | semidirect |
| 85. C4×C13 | #104 | semidirect |
| 94. #127 | #261 | semidirect |
| 138. C13 | #1980 | semidirect |
| 177. C4 | #88116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719421 | 2 |
| C2×#88116 | 2 |
| C4×C4⋊#261 | 2 |
| C4×#6118 | 2 |
| #1980 | 13 |