Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1072 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 258 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×C4⋊#261 | C2 | semidirect |
| 3. C22×D13⋊C8 | C2 | semidirect |
| 4. C2×#88115 | C2 | direct (N × H) |
| 7. C22×D4×C13 | C4 | semidirect |
| 11. C2×D4×D13 | C4 | semidirect |
| 13. C22×D52 | C4 | semidirect |
| 17. C2×C4⋊#261 | C22 | semidirect |
| 19. C2×D13⋊C8 | C22 | semidirect |
| 20. #88115 | C22 | direct (N × H) |
| 31. C2×D4×C13 | C2×C4 | semidirect |
| 39. D4×D13 | C2×C4 | semidirect |
| 42. C2×D52 | C2×C4 | semidirect |
| 49. C4⋊#261 | C23 | semidirect |
| 51. D13⋊C8 | C23 | semidirect |
| 70. D4×C13 | C22×C4 | semidirect |
| 78. D52 | C22×C4 | semidirect |
| 91. C22×C13 | #102 | semidirect |
| 98. C2×D13 | #102 | semidirect |
| 115. C22×D4 | #261 | semidirect |
| 125. C2×C13 | C2×#102 | semidirect |
| 128. D13 | C2×#102 | semidirect |
| 148. C2×D4 | C2×#261 | semidirect |
| 162. C13 | C22×#102 | semidirect |
| 182. D4 | C22×#261 | semidirect |
| 207. C22 | #88115 | direct (N × H) |
| 219. C2 | C2×#88115 | 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×C4⋊#261 | 2 |
| C22×D13⋊C8 | 2 |
| C2×#88115 | 2 |
| C22×#102 | 13 |