Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×Q16×D13 | C2 | semidirect |
| 3. C13×#494 | C2 | semidirect |
| 4. #11718849 | C2 | semidirect |
| 5. #11718847 | C2 | semidirect |
| 6. #11718751 | C2 | semidirect |
| 7. C4×Dic52 | C2 | semidirect |
| 53. Dic52 | D4 | semidirect |
| 66. D52 | Q16 | semidirect |
| 78. #494 | D13 | semidirect |
| 87. C2×D13 | C2×Q16 | semidirect |
| 90. C4×C13 | C2×Q16 | semidirect |
| 146. C13 | D4×Q16 | semidirect |
| 176. C4 | Q16×D13 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D13 | 2 |
| #11719432 | 2 |
| C13×#494 | 2 |
| #11718849 | 2 |
| #11718847 | 2 |
| #11718751 | 2 |
| C4×Dic52 | 2 |
| C8×D52 | 2 |
| D4×Q16 | 13 |