Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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×#88186 | C2 | semidirect |
| 2. C2×#88186 | C2 | semidirect |
| 3. #11719453 | C2 | semidirect |
| 4. #11719450 | C2 | semidirect |
| 5. C2×C13×#100 | C2 | semidirect |
| 6. #11718793 | C2 | semidirect |
| 7. #11718785 | C2 | semidirect |
| 8. #11718410 | C2 | semidirect |
| 9. #11718409 | C2 | semidirect |
| 16. C2×#6105 | C22 | semidirect |
| 22. C2×#6104 | C22 | semidirect |
| 26. #88163 | C22 | semidirect |
| 28. #88162 | C22 | semidirect |
| 29. #88161 | C22 | semidirect |
| 33. C13×#100 | C22 | semidirect |
| 34. #88064 | C22 | semidirect |
| 35. #88063 | C22 | semidirect |
| 36. #88062 | C22 | semidirect |
| 131. C2×#100 | D13 | semidirect |
| 176. #100 | C2×D13 | semidirect |
| 230. C13 | #3068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88186 | 2 |
| #11719453 | 2 |
| #11719450 | 2 |
| C2×C13×#100 | 2 |
| #11718793 | 2 |
| #11718785 | 2 |
| #11718410 | 2 |
| #11718409 | 2 |
| #3068 | 13 |