Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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. C4×C13×Q16 | C2 | semidirect |
| 4. #11718692 | C2 | semidirect |
| 5. #11718548 | C2 | semidirect |
| 6. #11718469 | C2 | semidirect |
| 7. #11718360 | C2 | semidirect |
| 37. C13×Q16 | D4 | semidirect |
| 66. D52 | Q16 | direct (N × H) |
| 82. C4×Q16 | D13 | semidirect |
| 87. C2×D13 | C2×Q16 | semidirect |
| 91. C4×C13 | C2×Q16 | semidirect |
| 131. Q16 | D52 | direct (N × H) |
| 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 |
| Q8×D52 | 2 |
| C4×C13×Q16 | 2 |
| #11718692 | 2 |
| #11718548 | 2 |
| #11718469 | 2 |
| #11718360 | 2 |
| C8×D52 | 2 |
| D4×Q16 | 13 |