Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1360 conjugacy classes of subgroups; only the 274 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 274 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×C22⋊#261 | C2 | semidirect |
| 3. C22×C4⋊#261 | C2 | semidirect |
| 4. C22×C4×#261 | C2 | semidirect |
| 5. #11719151 | C2 | direct (N × H) |
| 9. C22×D4×C13 | C4 | semidirect |
| 10. C22×C22⋊D13 | C4 | semidirect |
| 13. C2×D4×D13 | C4 | semidirect |
| 15. C22×D52 | C4 | semidirect |
| 18. C2×C22⋊#261 | C22 | semidirect |
| 20. C2×C4⋊#261 | C22 | semidirect |
| 22. C2×C4×#261 | C22 | semidirect |
| 36. C22×#261 | D4 | semidirect |
| 40. C2×D4×C13 | C2×C4 | semidirect |
| 43. C2×C22⋊D13 | C2×C4 | semidirect |
| 49. C2×D52 | C2×C4 | semidirect |
| 86. C2×#261 | C2×D4 | semidirect |
| 88. C2×C4×C13 | C22⋊C4 | semidirect |
| 91. C2×Dic13 | C22⋊C4 | semidirect |
| 94. C4×D13 | C22⋊C4 | semidirect |
| 126. C4×C13 | C2×C22⋊C4 | semidirect |
| 127. Dic13 | C2×C22⋊C4 | semidirect |
| 135. C22×D4 | #261 | semidirect |
| 146. C2×C13 | #390 | semidirect |
| 150. D13 | #390 | semidirect |
| 171. C2×D4 | C2×#261 | semidirect |
| 188. C13 | C2×#390 | semidirect |
| 226. C2×C4 | C22⋊#261 | semidirect |
| 253. C4 | C2×C22⋊#261 | semidirect |
| 260. C2 | #11719151 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D13 | 2 |
| C22×C22⋊#261 | 2 |
| C22×C4⋊#261 | 2 |
| C22×C4×#261 | 2 |
| #11719151 | 2 |
| C2×#390 | 13 |