Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
496 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×#88192 | C2 | semidirect |
| 2. C22×#6104 | C2 | semidirect |
| 3. C2×#88149 | C2 | semidirect |
| 4. C2×C13×#102 | C2 | semidirect |
| 5. C2×#88061 | C2 | semidirect |
| 6. C2×#88060 | C2 | semidirect |
| 7. #11718121 | C2 | semidirect |
| 37. C2×D4×C13 | D4 | semidirect |
| 53. C2×D52 | D4 | semidirect |
| 64. C13×C4⋊C4 | D4 | semidirect |
| 69. C4⋊Dic13 | D4 | semidirect |
| 72. C2×#1055 | D4 | semidirect |
| 95. C22×D13 | D8 | semidirect |
| 131. C2×#102 | D13 | semidirect |
| 220. C2×D4 | D52 | semidirect |
| 241. C4⋊C4 | C22⋊D13 | semidirect |
| 244. C13 | #1999 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88192 | 2 |
| C22×#6104 | 2 |
| C2×#88149 | 2 |
| C2×C13×#102 | 2 |
| C2×#88061 | 2 |
| C2×#88060 | 2 |
| #11718121 | 2 |
| #1999 | 13 |