Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
552 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 173 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×#88163 | C2 | semidirect |
| 3. C2×#88123 | C2 | semidirect |
| 4. C4×C13×M16 | C2 | semidirect |
| 5. #11718376 | C2 | semidirect |
| 6. #11718360 | C2 | semidirect |
| 7. #11718354 | C2 | semidirect |
| 38. C13×M16 | D4 | semidirect |
| 75. C4×M16 | D13 | semidirect |
| 83. C4×C13 | #137 | semidirect |
| 123. M16 | D52 | semidirect |
| 132. C13 | #3152 | semidirect |
| 161. C4 | #88163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88163 | 2 |
| #11719182 | 2 |
| C2×#88123 | 2 |
| C4×C13×M16 | 2 |
| #11718376 | 2 |
| #11718360 | 2 |
| #11718354 | 2 |
| #3152 | 13 |