Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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×C13×#127 | C2 | semidirect |
| 2. #11719510 | C2 | semidirect |
| 3. C2×#88186 | C2 | semidirect |
| 4. C2×#88073 | C2 | semidirect |
| 5. #11718876 | C2 | semidirect |
| 6. C2×#88045 | C2 | semidirect |
| 7. #11718115 | C2 | semidirect |
| 44. C2×D4×C13 | D4 | semidirect |
| 53. C2×D52 | D4 | semidirect |
| 55. C2×Dic26 | D4 | semidirect |
| 57. C42×C13 | D4 | semidirect |
| 62. C4⋊Dic13 | D4 | semidirect |
| 67. #6099 | D4 | semidirect |
| 113. C2×#127 | D13 | semidirect |
| 190. C2×D4 | C22⋊D13 | semidirect |
| 207. C42 | C22⋊D13 | semidirect |
| 208. C13 | #2002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#127 | 2 |
| #11719510 | 2 |
| C2×#88186 | 2 |
| C2×#88073 | 2 |
| #11718876 | 2 |
| C2×#88045 | 2 |
| #11718115 | 2 |
| #2002 | 13 |