Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. #11718492 | C2 | semidirect |
| 4. C13×#335 | C2 | semidirect |
| 5. #11718076 | C2 | semidirect |
| 7. #11718047 | C2 | semidirect |
| 58. C8×C13 | M16 | semidirect |
| 65. #335 | D13 | semidirect |
| 118. C13 | #1592 | semidirect |
| 138. C8 | #6094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11718499 | 2 |
| #11718492 | 2 |
| C4×#6095 | 2 |
| C13×#335 | 2 |
| #11718076 | 2 |
| #11718075 | 2 |
| #11718047 | 2 |
| #1592 | 13 |