Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
290 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 3. C2×#88102 | C2 | semidirect |
| 4. C4⋊C4×#261 | C2 | semidirect |
| 6. (C2×#261)⋊C8 | C2 | semidirect |
| 7. #11718246 | C2 | semidirect |
| 21. C13×#102 | C4 | semidirect |
| 22. #88072 | C4 | semidirect |
| 23. #88061 | C4 | semidirect |
| 24. #88049 | C4 | semidirect |
| 148. #102 | #261 | semidirect |
| 192. C13 | #1925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719151 | 2 |
| C2×#88115 | 2 |
| C2×#88102 | 2 |
| C4⋊C4×#261 | 2 |
| D13×#102 | 2 |
| (C2×#261)⋊C8 | 2 |
| #11718246 | 2 |
| #1925 | 13 |