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. C13×#535 | C2 | semidirect |
| 2. C2×#88203 | C2 | semidirect |
| 3. C2×#88194 | C2 | semidirect |
| 4. C2×#88077 | C2 | semidirect |
| 5. C2×#88073 | C2 | semidirect |
| 6. #11718662 | C2 | semidirect |
| 7. #11718124 | C2 | semidirect |
| 35. C2×Q8×C13 | D4 | semidirect |
| 44. C2×D4×C13 | D4 | semidirect |
| 55. C2×D52 | D4 | semidirect |
| 56. C13×C4⋊C4 | D4 | semidirect |
| 63. C4×Dic13 | D4 | semidirect |
| 67. #6099 | D4 | semidirect |
| 112. #535 | D13 | semidirect |
| 173. C2×Q8 | C22⋊D13 | semidirect |
| 190. C2×D4 | C22⋊D13 | semidirect |
| 202. C4⋊C4 | 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 |
|---|---|
| C13×#535 | 2 |
| C2×#88203 | 2 |
| C2×#88194 | 2 |
| C2×#88077 | 2 |
| C2×#88073 | 2 |
| #11718662 | 2 |
| #11718124 | 2 |
| #2002 | 13 |