Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
348 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 107 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. C13×#391 | C2 | semidirect |
| 3. C2×#88075 | C2 | semidirect |
| 5. C2×#88048 | C2 | semidirect |
| 7. C2×C4×#1055 | C2 | semidirect |
| 14. C2×#6106 | C4 | semidirect |
| 74. C2×C4×C13 | SD16 | semidirect |
| 88. #1055 | C22⋊C4 | semidirect |
| 94. #391 | D13 | semidirect |
| 168. C13 | #1968 | semidirect |
| 192. C2×C4 | #6106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6106 | 2 |
| C13×#391 | 2 |
| C2×#88075 | 2 |
| C2×#88049 | 2 |
| C2×#88048 | 2 |
| #11718600 | 2 |
| C2×C4×#1055 | 2 |
| #1968 | 13 |