Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
512 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
| 5. C2×C13×#103 | C2 | semidirect |
| 6. C2×#88056 | C2 | semidirect |
| 7. C2×#88047 | C2 | semidirect |
| 8. #11718474 | C2 | direct (N × H) |
| 17. C2×#6107 | C22 | semidirect |
| 28. C13×#103 | C22 | semidirect |
| 29. #88056 | C22 | semidirect |
| 30. #88047 | C22 | semidirect |
| 68. C22×D13 | Q16 | semidirect |
| 102. C2×#103 | D13 | semidirect |
| 110. C2×D13 | C2×Q16 | semidirect |
| 140. #103 | C2×D13 | semidirect |
| 141. C2×C13 | #467 | semidirect |
| 179. C13 | C2×#467 | semidirect |
| 227. C2 | #11718474 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88200 | 2 |
| C22×#6107 | 2 |
| C22×C8×D13 | 2 |
| C2×#88151 | 2 |
| C2×C13×#103 | 2 |
| C2×#88056 | 2 |
| C2×#88047 | 2 |
| #11718474 | 2 |
| C2×#467 | 13 |