Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 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. C13×#436 | C2 | semidirect |
| 3. #11718349 | C2 | semidirect |
| 4. D4⋊#1055 | C2 | semidirect |
| 5. #11718075 | C2 | semidirect |
| 6. #11718071 | C2 | semidirect |
| 7. C8×#1055 | C2 | semidirect |
| 60. C8×C13 | D8 | semidirect |
| 64. #1055 | M16 | semidirect |
| 67. #436 | D13 | semidirect |
| 125. C13 | #1589 | semidirect |
| 147. C8 | #6104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#436 | 2 |
| C4×#6104 | 2 |
| #11718349 | 2 |
| D4⋊#1055 | 2 |
| #11718075 | 2 |
| #11718071 | 2 |
| C8×#1055 | 2 |
| #1589 | 13 |