Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
384 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 157 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×C4×C8×C13 | C2 | semidirect |
| 4. C2×C8×Dic13 | C2 | semidirect |
| 6. #11718142 | C2 | semidirect |
| 7. #11718116 | C2 | semidirect |
| 18. C2×C8×D13 | C4 | semidirect |
| 21. #88060 | C4 | semidirect |
| 42. #6103 | C8 | direct (N × H) |
| 61. C2×C4×C13 | C2×C8 | semidirect |
| 73. C2×Dic13 | C2×C8 | semidirect |
| 79. C8×C13 | C22⋊C4 | semidirect |
| 85. C2×C4×C8 | D13 | semidirect |
| 98. C2×D13 | C4×C8 | semidirect |
| 156. C13 | C8×C22⋊C4 | semidirect |
| 175. C2×C4 | C8×D13 | semidirect |
| 185. C8 | #6103 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D13 | 2 |
| C2×C4×C8×C13 | 2 |
| C2×#88060 | 2 |
| C2×C8×Dic13 | 2 |
| C4×#6103 | 2 |
| #11718142 | 2 |
| #11718116 | 2 |
| C8×C22⋊C4 | 13 |