Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
848 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 104 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×#88115 | C2 | semidirect |
| 3. #11719136 | C2 | semidirect |
| 4. D13⋊(C22⋊C8) | C2 | semidirect |
| 6. C22×D4×C13 | C4 | semidirect |
| 11. C2×D4×D13 | C4 | semidirect |
| 13. C22×D52 | C4 | semidirect |
| 16. C2×C4⋊#261 | C22 | semidirect |
| 17. C2×D13⋊C8 | C22 | semidirect |
| 88. D4×C13 | C22⋊C4 | semidirect |
| 99. D52 | C22⋊C4 | semidirect |
| 115. C22×C13 | #102 | semidirect |
| 128. C2×D13 | #102 | semidirect |
| 146. C22×D4 | #261 | semidirect |
| 200. C13 | #1786 | semidirect |
| 232. D4 | C22⋊#261 | semidirect |
| 269. C22 | #88115 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D13 | 2 |
| C2×#88115 | 2 |
| #11719136 | 2 |
| D13⋊(C22⋊C8) | 2 |
| #1786 | 13 |