Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
772 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 202 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. C2×#88237 | C2 | semidirect |
| 3. C2×D13⋊M16 | C2 | semidirect |
| 4. #11719155 | C2 | direct (N × H) |
| 5. C2×#88118 | C2 | semidirect |
| 6. C22×Q8×C13 | C4 | semidirect |
| 11. C2×#6131 | C4 | semidirect |
| 12. C2×#6131 | C4 | semidirect |
| 16. C22×D52 | C4 | semidirect |
| 22. #88237 | C22 | semidirect |
| 24. C2×C4×#261 | C22 | semidirect |
| 26. D13⋊M16 | C22 | semidirect |
| 27. C2×#6118 | C22 | semidirect |
| 29. #88118 | C22 | semidirect |
| 36. C2×Q8×C13 | C2×C4 | semidirect |
| 48. #6131 | C2×C4 | semidirect |
| 57. C2×D52 | C2×C4 | semidirect |
| 75. C4×#261 | C23 | semidirect |
| 77. #6118 | C23 | semidirect |
| 158. C22×Q8 | #261 | semidirect |
| 175. C2×C13 | #421 | semidirect |
| 196. C2×Q8 | C2×#261 | semidirect |
| 230. C13 | C2×#421 | semidirect |
| 301. C2 | #11719155 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6131 | 2 |
| C2×#88237 | 2 |
| C2×D13⋊M16 | 2 |
| #11719155 | 2 |
| C2×#88118 | 2 |
| C2×#421 | 13 |