Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#6107 | C2 | semidirect |
| 4. C2×#88141 | C2 | semidirect |
| 5. C2×C13×#103 | C2 | semidirect |
| 6. C2×#88054 | C2 | semidirect |
| 8. #11718459 | C2 | direct (N × H) |
| 17. C2×#6107 | C22 | semidirect |
| 27. #88141 | C22 | semidirect |
| 28. C13×#103 | C22 | semidirect |
| 29. #88054 | C22 | semidirect |
| 101. C2×#103 | D13 | semidirect |
| 139. #103 | C2×D13 | semidirect |
| 141. C2×C13 | #464 | semidirect |
| 179. C13 | C2×#464 | semidirect |
| 227. C2 | #11718459 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88201 | 2 |
| C22×#6107 | 2 |
| C22×#6095 | 2 |
| C2×#88141 | 2 |
| C2×C13×#103 | 2 |
| C2×#88054 | 2 |
| C2×#88049 | 2 |
| #11718459 | 2 |
| C2×#464 | 13 |