Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1072 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 349 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×C4⋊Dic31 | C2 | semidirect |
| 3. C2×#11758409 | C2 | direct (N × H) |
| 4. C23×C8×C31 | C2 | semidirect |
| 10. C22×D124 | C4 | semidirect |
| 13. C22×C8×C31 | C22 | semidirect |
| 15. C2×C4⋊Dic31 | C22 | semidirect |
| 16. #11758409 | C22 | direct (N × H) |
| 31. C2×D124 | C2×C4 | semidirect |
| 34. C2×C8×C31 | C23 | semidirect |
| 36. C4⋊Dic31 | C23 | semidirect |
| 55. D124 | C22×C4 | semidirect |
| 58. C22×C31 | #102 | semidirect |
| 72. C23×C8 | D31 | semidirect |
| 75. C2×C31 | C2×#102 | semidirect |
| 88. C22×C8 | C2×D31 | semidirect |
| 92. C31 | C22×#102 | semidirect |
| 110. C2×C8 | C22×D31 | semidirect |
| 137. C22 | #11758409 | direct (N × H) |
| 147. C2 | C2×#11758409 | 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×C4⋊Dic31 | 2 |
| C2×#11758409 | 2 |
| C23×C8×C31 | 2 |
| C22×#102 | 31 |