Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
456 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 225 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. C8×Q8×C13 | C2 | semidirect |
| 3. Q8×#1055 | C2 | semidirect |
| 4. #11718495 | C2 | semidirect |
| 5. #11718494 | C2 | semidirect |
| 6. C8×D52 | C2 | semidirect |
| 7. C4×C8×D13 | C2 | semidirect |
| 25. #6131 | C8 | direct (N × H) |
| 45. Q8×C13 | C2×C8 | semidirect |
| 52. D52 | C2×C8 | semidirect |
| 56. C4×D13 | C2×C8 | semidirect |
| 58. C8×C13 | #41 | semidirect |
| 60. #1055 | #41 | semidirect |
| 63. C8×Q8 | D13 | semidirect |
| 118. C13 | C8×#41 | semidirect |
| 120. Q8 | C8×D13 | semidirect |
| 135. C8 | #6131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6131 | 2 |
| C8×Q8×C13 | 2 |
| Q8×#1055 | 2 |
| #11718495 | 2 |
| #11718494 | 2 |
| C8×D52 | 2 |
| C4×C8×D13 | 2 |
| C8×#41 | 13 |