Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
168 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 74 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. #11718221 | C2 | direct (N × H) |
| 8. C2×C13×C16 | C4 | semidirect |
| 9. C2×#6090 | C4 | semidirect |
| 10. C16×D13 | C4 | semidirect |
| 22. C13×C16 | C2×C4 | semidirect |
| 23. #6090 | C2×C4 | semidirect |
| 56. C2×C16 | #261 | semidirect |
| 59. C2×C13 | #366 | semidirect |
| 61. D13 | #366 | semidirect |
| 75. C16 | C2×#261 | semidirect |
| 76. C13 | C2×#366 | semidirect |
| 103. C2 | #11718221 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88102 | 2 |
| C2×C16×D13 | 2 |
| #11718221 | 2 |
| C2×#366 | 13 |