Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
340 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 68 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. #11719136 | C2 | semidirect |
| 3. C2×#88111 | C2 | semidirect |
| 4. #11718292 | C2 | semidirect |
| 5. #11718240 | C2 | semidirect |
| 7. C2×D4×D13 | C4 | semidirect |
| 12. C13×#121 | C4 | semidirect |
| 15. #88184 | C4 | semidirect |
| 17. C4⋊C4×D13 | C4 | semidirect |
| 20. (C2×#261)⋊C4 | C22 | semidirect |
| 22. #88111 | C22 | semidirect |
| 135. #121 | #261 | semidirect |
| 184. C13 | #1519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D13×#121 | 2 |
| #11719136 | 2 |
| C2×#88111 | 2 |
| #11718292 | 2 |
| #11718240 | 2 |
| #1519 | 13 |