Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
388 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C2×#88100 | C2 | semidirect |
| 4. C4⋊C4×#261 | C2 | semidirect |
| 6. #11718265 | C2 | semidirect |
| 7. #11718246 | C2 | semidirect |
| 12. D4×#261 | C4 | semidirect |
| 20. #88115 | C4 | semidirect |
| 23. C13×#102 | C4 | semidirect |
| 24. #88072 | C4 | semidirect |
| 25. #88061 | C4 | semidirect |
| 26. #88049 | C4 | semidirect |
| 49. C4⋊#261 | C2×C4 | semidirect |
| 54. D13⋊C8 | C2×C4 | semidirect |
| 55. C2×C8×C13 | C2×C4 | semidirect |
| 56. C13×C4⋊C4 | C2×C4 | semidirect |
| 57. C4⋊Dic13 | C2×C4 | semidirect |
| 59. C2×#1055 | C2×C4 | semidirect |
| 86. D4×C13 | C42 | semidirect |
| 94. D52 | C42 | semidirect |
| 154. #102 | #261 | semidirect |
| 189. C2×C8 | C2×#261 | semidirect |
| 196. C4⋊C4 | C2×#261 | semidirect |
| 201. C13 | #1762 | semidirect |
| 216. D4 | C4×#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×#88115 | 2 |
| C2×#88100 | 2 |
| C4⋊C4×#261 | 2 |
| D13×#102 | 2 |
| #11718265 | 2 |
| #11718246 | 2 |
| #1762 | 13 |