Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1252 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 253 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×#6103 | C2 | semidirect |
| 3. C22×#6103 | C2 | semidirect |
| 4. C22×#6101 | C2 | semidirect |
| 5. C2×C13×#95 | C2 | semidirect |
| 6. #11718333 | C2 | direct (N × H) |
| 17. C2×#6103 | C22 | semidirect |
| 18. C2×#6103 | C22 | semidirect |
| 20. C2×#6101 | C22 | semidirect |
| 21. C13×#95 | C22 | semidirect |
| 42. C22×Dic13 | D4 | semidirect |
| 85. C2×Dic13 | C2×D4 | semidirect |
| 92. C2×#95 | D13 | semidirect |
| 129. #95 | C2×D13 | semidirect |
| 130. C2×C13 | #394 | semidirect |
| 166. C13 | C2×#394 | semidirect |
| 225. C2 | #11718333 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D52 | 2 |
| C22×#6103 | 2 |
| C22×#6101 | 2 |
| C2×C13×#95 | 2 |
| #11718333 | 2 |
| C2×#394 | 13 |