Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1048 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×D124 | C2 | semidirect |
| 2. C22×D248 | C2 | semidirect |
| 3. C2×#11758507 | C2 | semidirect |
| 4. #14521185 | C2 | direct (N × H) |
| 5. C2×#11758409 | C2 | semidirect |
| 6. C2×C31×C22⋊C8 | C2 | semidirect |
| 14. C22×D124 | C22 | semidirect |
| 15. C22×D124 | C22 | semidirect |
| 16. C22×C8×C31 | C22 | semidirect |
| 18. #11758507 | C22 | semidirect |
| 20. C2×C4⋊Dic31 | C22 | semidirect |
| 22. C2×D248 | C22 | semidirect |
| 23. C31×C22⋊C8 | C22 | semidirect |
| 24. #11758409 | C22 | semidirect |
| 48. C2×D124 | D4 | semidirect |
| 50. C2×D124 | C23 | semidirect |
| 52. C2×C8×C31 | C23 | semidirect |
| 55. C4⋊Dic31 | C23 | semidirect |
| 59. C23×C31 | D8 | semidirect |
| 89. D124 | C2×D4 | semidirect |
| 97. C22×C31 | C2×D8 | semidirect |
| 118. C2×C22⋊C8 | D31 | semidirect |
| 120. C2×C31 | #447 | semidirect |
| 137. C22×C8 | C2×D31 | semidirect |
| 143. C22⋊C8 | C2×D31 | semidirect |
| 144. C31 | C2×#447 | semidirect |
| 173. C2×C8 | C22×D31 | semidirect |
| 191. C23 | D248 | semidirect |
| 225. C22 | C2×D248 | semidirect |
| 235. C2 | #14521185 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D124 | 2 |
| C22×D248 | 2 |
| C2×#11758507 | 2 |
| #14521185 | 2 |
| C2×#11758409 | 2 |
| C2×C31×C22⋊C8 | 2 |
| C2×#447 | 31 |