Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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×#6105 | C2 | semidirect |
| 3. C2×#88178 | C2 | semidirect |
| 4. C2×#88072 | C2 | semidirect |
| 5. C2×C22⋊#1055 | C2 | semidirect |
| 6. C2×#88050 | C2 | semidirect |
| 7. #11718121 | C2 | semidirect |
| 56. C2×Dic26 | D4 | semidirect |
| 63. C4⋊Dic13 | D4 | semidirect |
| 70. C2×#1055 | D4 | semidirect |
| 85. C23×C13 | SD16 | semidirect |
| 228. C13 | #2000 | semidirect |
| 242. C23 | #6105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#121 | 2 |
| C22×#6105 | 2 |
| C2×#88178 | 2 |
| C2×#88072 | 2 |
| C2×C22⋊#1055 | 2 |
| C2×#88050 | 2 |
| #11718121 | 2 |
| #2000 | 13 |