Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
400 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×C13×Q16 | C2 | semidirect |
| 3. C2×#88068 | C2 | direct (N × H) |
| 4. C22×#6090 | C2 | semidirect |
| 8. C2×C13×Q16 | C22 | semidirect |
| 12. #88068 | C22 | direct (N × H) |
| 13. C2×#6090 | C22 | semidirect |
| 22. C13×Q16 | C23 | semidirect |
| 27. #6090 | C23 | semidirect |
| 41. C22×Q16 | D13 | semidirect |
| 45. C22×C13 | SD32 | semidirect |
| 55. C2×Q16 | C2×D13 | semidirect |
| 61. C2×C13 | C2×SD32 | semidirect |
| 72. Q16 | C22×D13 | semidirect |
| 78. C13 | C22×SD32 | semidirect |
| 93. C22 | #88068 | direct (N × H) |
| 99. C2 | C2×#88068 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×Q16 | 2 |
| C22×D104 | 2 |
| C2×#88068 | 2 |
| C22×#6090 | 2 |
| C22×SD32 | 13 |