Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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. C22×#6095 | C2 | semidirect |
| 2. C2×#88155 | C2 | semidirect |
| 3. #11719231 | C2 | semidirect |
| 5. C13×#427 | C2 | semidirect |
| 6. #11718665 | C2 | semidirect |
| 7. #11718662 | C2 | semidirect |
| 8. #11718547 | C2 | semidirect |
| 9. #11718525 | C2 | semidirect |
| 21. C2×#6094 | C22 | semidirect |
| 22. C2×C8×D13 | C22 | semidirect |
| 23. #88151 | C22 | semidirect |
| 31. C13×#107 | C22 | semidirect |
| 32. C13×#106 | C22 | semidirect |
| 33. #88050 | C22 | semidirect |
| 53. C2×C8×C13 | D4 | semidirect |
| 107. #427 | D13 | semidirect |
| 146. #107 | C2×D13 | semidirect |
| 147. #106 | C2×D13 | semidirect |
| 179. C2×C8 | D52 | semidirect |
| 191. C13 | #3057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6095 | 2 |
| C2×#88155 | 2 |
| #11719231 | 2 |
| #11719230 | 2 |
| C13×#427 | 2 |
| #11718665 | 2 |
| #11718662 | 2 |
| #11718547 | 2 |
| #11718525 | 2 |
| #3057 | 13 |