Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 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×#88173 | C2 | semidirect |
| 2. C2×C13×Q32 | C2 | semidirect |
| 3. C2×#88068 | C2 | semidirect |
| 4. #11718580 | C2 | direct (N × H) |
| 5. C2×D208 | C2 | semidirect |
| 6. C2×C16×D13 | C2 | semidirect |
| 11. #88173 | C22 | semidirect |
| 14. C13×Q32 | C22 | semidirect |
| 16. #88068 | C22 | semidirect |
| 18. D208 | C22 | semidirect |
| 19. C16×D13 | C22 | semidirect |
| 57. C2×Q32 | D13 | semidirect |
| 77. Q32 | C2×D13 | semidirect |
| 83. C2×C13 | #508 | semidirect |
| 105. C13 | C2×#508 | semidirect |
| 133. C2 | #11718580 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88173 | 2 |
| C2×C13×Q32 | 2 |
| C2×#88068 | 2 |
| #11718580 | 2 |
| C2×D208 | 2 |
| C2×C16×D13 | 2 |
| C2×#508 | 13 |