Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
496 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 93 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×D248 | C2 | semidirect |
| 2. C2×#11758472 | C2 | semidirect |
| 3. C2×#11758397 | C2 | semidirect |
| 4. C2×(C2×D31)⋊C8 | C2 | semidirect |
| 5. C31×#340 | C2 | semidirect |
| 32. C2×D124 | D4 | semidirect |
| 38. C2×C8×C31 | D4 | semidirect |
| 40. C4⋊C4×C31 | D4 | semidirect |
| 57. C22×D31 | D8 | semidirect |
| 104. #340 | D31 | semidirect |
| 125. C31 | #1999 | semidirect |
| 148. C2×C8 | D124 | semidirect |
| 150. C4⋊C4 | D124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D248 | 2 |
| C2×#11758472 | 2 |
| C2×#11758397 | 2 |
| C2×(C2×D31)⋊C8 | 2 |
| C31×#340 | 2 |
| #1999 | 31 |