Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
332 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 113 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×C22⋊#1055 | C2 | semidirect |
| 3. #11718120 | C2 | semidirect |
| 4. #11718117 | C2 | semidirect |
| 21. C2×D4×C13 | C8 | semidirect |
| 49. C23×C13 | C2×C8 | semidirect |
| 67. C2×C4×C13 | C2×C8 | semidirect |
| 118. C2×D4 | #1055 | semidirect |
| 137. C13 | #1459 | semidirect |
| 145. C23 | C2×#1055 | semidirect |
| 162. C2×C4 | C2×#1055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C13 | 2 |
| C2×C22⋊#1055 | 2 |
| #11718120 | 2 |
| #11718117 | 2 |
| #1459 | 13 |