Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
442 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 76 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. C22×C4×#261 | C2 | semidirect |
| 3. C2×#88118 | C2 | semidirect |
| 4. #11719127 | C2 | semidirect |
| 5. #11718247 | C2 | semidirect |
| 13. C13×C22⋊Q8 | C4 | semidirect |
| 14. #88200 | C4 | semidirect |
| 15. #88184 | C4 | semidirect |
| 16. #88149 | C4 | semidirect |
| 30. C2×Q8×C13 | C2×C4 | semidirect |
| 38. C2×D52 | C2×C4 | semidirect |
| 49. C4×#261 | D4 | semidirect |
| 53. C13×C4⋊C4 | C2×C4 | semidirect |
| 59. C4⋊Dic13 | C2×C4 | semidirect |
| 105. C22×C13 | #104 | semidirect |
| 116. C2×D13 | #104 | semidirect |
| 133. C22⋊Q8 | #261 | semidirect |
| 157. C2×Q8 | C2×#261 | semidirect |
| 181. C4⋊C4 | C2×#261 | semidirect |
| 191. C13 | #1896 | semidirect |
| 241. C22 | #88118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#261 | 2 |
| #11719332 | 2 |
| C2×#88118 | 2 |
| #11719127 | 2 |
| #11718247 | 2 |
| #1896 | 13 |