Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
184 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C31 | C2×D16 |
| commutator | C16 | C22×C4×C31 |
| Frattini, cosocle | C2×C16 | C23×C31 |
| socle | C2×C31 | C4×D16 |
| prime radical | C31×#2262 | C2 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C31 ◁ C2×C8×C31 ◁ C4×C8×C31 ◁ C4×C16×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C31×#2178 | C2 | semidirect |
| 3. C31×#1425 | C2 | semidirect |
| 4. C31×#1417 | C2 | semidirect |
| 5. C31×#1397 | C2 | semidirect |
| 8. C31×Q64 | C4 | semidirect |
| 9. C31×SD64 | C4 | semidirect |
| 10. C31×D32 | C4 | semidirect |
| 42. #13656 | C31 | direct (N × H) |
| 54. #2178 | C2×C31 | semidirect |
| 55. #1425 | C2×C31 | semidirect |
| 56. #1417 | C2×C31 | semidirect |
| 57. #1397 | C2×C31 | semidirect |
| 66. Q64 | C4×C31 | semidirect |
| 67. SD64 | C4×C31 | semidirect |
| 68. D32 | C4×C31 | semidirect |
| 90. C31 | #13656 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#2262 | 2 |
| C31×#2178 | 2 |
| C31×#1425 | 2 |
| C31×#1417 | 2 |
| C31×#1397 | 2 |
| #13656 | 31 |