Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
272 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 101 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×C13×#107 | C2 | semidirect |
| 3. C22×#6090 | C2 | semidirect |
| 4. #11718083 | C2 | direct (N × H) |
| 10. C2×D104 | C4 | semidirect |
| 13. C13×#107 | C22 | semidirect |
| 15. C2×#6090 | C22 | semidirect |
| 31. D104 | C2×C4 | semidirect |
| 53. C2×#107 | D13 | semidirect |
| 77. #107 | C2×D13 | semidirect |
| 78. C2×C13 | #357 | semidirect |
| 100. C13 | C2×#357 | semidirect |
| 131. C2 | #11718083 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D104 | 2 |
| C2×C13×#107 | 2 |
| C22×#6090 | 2 |
| #11718083 | 2 |
| C2×#357 | 13 |