Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
348 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 112 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×#88110 | C2 | semidirect |
| 4. C2×C4×#1057 | C2 | semidirect |
| 6. #11718290 | C2 | semidirect |
| 7. #11718290 | C2 | semidirect |
| 15. C2×#6118 | C4 | semidirect |
| 20. #88111 | C4 | semidirect |
| 74. C2×C4×C13 | M16 | semidirect |
| 80. C2×Dic13 | M16 | semidirect |
| 94. #1057 | C22⋊C4 | semidirect |
| 182. C13 | #1753 | semidirect |
| 214. C2×C4 | #6118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6118 | 2 |
| C2×#88111 | 2 |
| C2×#88110 | 2 |
| C2×C4×#1057 | 2 |
| #11718327 | 2 |
| #11718290 | 2 |
| #1753 | 13 |