Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
924 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 210 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×D4×#261 | C2 | semidirect |
| 3. #11719151 | C2 | semidirect |
| 4. #11719059 | C2 | semidirect |
| 5. C42×#261 | C2 | semidirect |
| 13. C13×#127 | C4 | semidirect |
| 14. #88194 | C4 | semidirect |
| 15. #88128 | C4 | semidirect |
| 22. C2×D4×C13 | C2×C4 | semidirect |
| 23. C2×C22⋊D13 | C2×C4 | semidirect |
| 26. C2×D52 | C2×C4 | semidirect |
| 31. C4×#261 | D4 | semidirect |
| 32. C42×C13 | C2×C4 | semidirect |
| 33. C4×Dic13 | C2×C4 | semidirect |
| 66. #261 | #127 | direct (N × H) |
| 67. C4×C13 | C4×D4 | semidirect |
| 68. Dic13 | C4×D4 | semidirect |
| 73. #127 | #261 | direct (N × H) |
| 90. C2×D4 | C2×#261 | semidirect |
| 101. C42 | C2×#261 | semidirect |
| 102. C13 | C4×#127 | semidirect |
| 131. C4 | D4×#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#261 | 2 |
| D13×#127 | 2 |
| #11719151 | 2 |
| #11719059 | 2 |
| C42×#261 | 2 |
| C4×#127 | 13 |