Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1224 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 277 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. C24×C4×C13 | C2 | semidirect |
| 3. C2×C4×C22⋊D13 | C2 | semidirect |
| 4. #11718908 | C2 | semidirect |
| 5. #11718874 | C2 | semidirect |
| 6. #11718871 | C2 | semidirect |
| 7. C4×C22⋊Dic13 | C2 | semidirect |
| 13. C22×C4×D13 | C22 | semidirect |
| 14. #88207 | C4 | direct (N × H) |
| 19. C2×#6103 | C22 | semidirect |
| 20. C2×#6101 | C22 | semidirect |
| 21. C2×C4×Dic13 | C22 | semidirect |
| 22. #88071 | C22 | semidirect |
| 25. C24×C13 | C2×C4 | semidirect |
| 32. C22×C4×C13 | D4 | semidirect |
| 37. C2×C22⋊D13 | C2×C4 | semidirect |
| 44. C22⋊Dic13 | C2×C4 | semidirect |
| 60. C22×D13 | C22×C4 | semidirect |
| 72. C2×Dic13 | C22×C4 | semidirect |
| 74. C24×C4 | D13 | semidirect |
| 86. C22×C13 | C4×D4 | semidirect |
| 94. C4×C13 | #120 | semidirect |
| 121. C24 | C4×D13 | semidirect |
| 134. C22×C4 | C22⋊D13 | semidirect |
| 143. C13 | C4×#120 | semidirect |
| 177. C22 | C4×C22⋊D13 | semidirect |
| 185. C4 | #88207 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C13 | 2 |
| C2×#88207 | 2 |
| C2×C4×C22⋊D13 | 2 |
| #11718908 | 2 |
| #11718874 | 2 |
| #11718871 | 2 |
| C4×C22⋊Dic13 | 2 |
| C4×#120 | 13 |