Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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×#88194 | C2 | semidirect |
| 2. C2×#88186 | C2 | semidirect |
| 3. #11719230 | C2 | semidirect |
| 4. C13×#418 | C2 | semidirect |
| 5. C2×#88065 | C2 | semidirect |
| 6. C2×#88063 | C2 | semidirect |
| 7. #11718124 | C2 | semidirect |
| 36. C2×D4×C13 | D4 | semidirect |
| 53. C2×D52 | D4 | semidirect |
| 55. C2×Dic26 | D4 | semidirect |
| 59. C13×C4⋊C4 | D4 | semidirect |
| 66. C4×Dic13 | D4 | semidirect |
| 68. #6099 | D4 | semidirect |
| 115. #418 | D13 | semidirect |
| 190. C2×D4 | D52 | 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 |
|---|---|
| C2×#88194 | 2 |
| C2×#88186 | 2 |
| #11719230 | 2 |
| C13×#418 | 2 |
| C2×#88065 | 2 |
| C2×#88063 | 2 |
| #11718124 | 2 |
| #2002 | 13 |