Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
438 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. C2×D4×#261 | C2 | semidirect |
| 3. #11719151 | C2 | semidirect |
| 4. C2×#88115 | C2 | semidirect |
| 5. C2×#88115 | C2 | semidirect |
| 6. #11718265 | C2 | semidirect |
| 7. (C2×#261)⋊C8 | C2 | semidirect |
| 20. C2×C13×D8 | C4 | semidirect |
| 21. C2×#6104 | C4 | semidirect |
| 22. C2×#6104 | C4 | semidirect |
| 25. C2×D104 | C4 | semidirect |
| 39. C2×D4×C13 | C2×C4 | semidirect |
| 51. C2×D52 | C2×C4 | semidirect |
| 66. C2×C8×C13 | C2×C4 | semidirect |
| 69. C2×#1055 | C2×C4 | semidirect |
| 103. C2×#261 | D8 | semidirect |
| 107. D4×C13 | C22⋊C4 | semidirect |
| 117. D52 | C22⋊C4 | semidirect |
| 175. C2×D8 | #261 | semidirect |
| 214. C2×D4 | C2×#261 | semidirect |
| 233. C2×C8 | C2×#261 | semidirect |
| 243. C13 | #1879 | semidirect |
| 272. D4 | C22⋊#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#261 | 2 |
| C2×D8×D13 | 2 |
| #11719151 | 2 |
| C2×#88115 | 2 |
| #11718265 | 2 |
| (C2×#261)⋊C8 | 2 |
| #1879 | 13 |