Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1464 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 525 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 |
|---|---|---|
| 2. C22×Q8×D13 | C2 | semidirect |
| 3. C22×C13×Q16 | C2 | semidirect |
| 4. C22×#6107 | C2 | semidirect |
| 5. C22×#6106 | C2 | semidirect |
| 6. C2×#88172 | C2 | direct (N × H) |
| 7. C22×#6095 | C2 | semidirect |
| 8. C22×#6094 | C2 | semidirect |
| 14. C2×Q8×D13 | C22 | semidirect |
| 22. C2×C13×Q16 | C22 | semidirect |
| 24. C2×#6107 | C22 | semidirect |
| 25. C2×#6106 | C22 | semidirect |
| 27. #88172 | C22 | direct (N × H) |
| 28. C2×#6095 | C22 | semidirect |
| 29. C2×#6094 | C22 | semidirect |
| 44. Q8×D13 | C23 | semidirect |
| 55. C13×Q16 | C23 | semidirect |
| 57. #6107 | C23 | semidirect |
| 58. #6106 | C23 | semidirect |
| 60. #6095 | C23 | semidirect |
| 61. #6094 | C23 | semidirect |
| 94. C22×Q16 | D13 | semidirect |
| 98. C22×C13 | #137 | semidirect |
| 125. C2×Q16 | C2×D13 | semidirect |
| 131. C2×C13 | C2×#137 | semidirect |
| 161. Q16 | C22×D13 | semidirect |
| 167. C13 | C22×#137 | semidirect |
| 199. C22 | #88172 | direct (N × H) |
| 209. C2 | C2×#88172 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6131 | 2 |
| C22×Q8×D13 | 2 |
| C22×C13×Q16 | 2 |
| C22×#6107 | 2 |
| C22×#6106 | 2 |
| C2×#88172 | 2 |
| C22×#6095 | 2 |
| C22×#6094 | 2 |
| C22×#137 | 13 |