Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
284 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | #2184 |
| commutator, Frattini, cosocle | C2×C16 | C23×C31 |
| prime radical | C31×#3415 | C2 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C31×#131 ◁ C31×#504 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C31×#2264 | C2 | semidirect |
| 3. C2×C31×SD64 | C2 | semidirect |
| 4. C31×#2222 | C2 | semidirect |
| 5. C31×#1419 | C2 | semidirect |
| 6. C31×#1417 | C2 | semidirect |
| 7. C31×#1401 | C2 | semidirect |
| 13. C2×C31×Q32 | C22 | semidirect |
| 21. C31×M64 | C22 | semidirect |
| 22. C2×C31×C32 | C22 | semidirect |
| 23. C31×#368 | C22 | semidirect |
| 80. #13671 | C31 | direct (N × H) |
| 105. #2264 | C2×C31 | semidirect |
| 106. C2×SD64 | C2×C31 | semidirect |
| 107. #2222 | C2×C31 | semidirect |
| 108. #1419 | C2×C31 | semidirect |
| 109. #1417 | C2×C31 | semidirect |
| 110. #1401 | C2×C31 | semidirect |
| 127. C2×Q32 | C22×C31 | semidirect |
| 135. M64 | C22×C31 | semidirect |
| 136. C2×C32 | C22×C31 | semidirect |
| 137. #368 | C22×C31 | semidirect |
| 171. C31 | #13671 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#3415 | 2 |
| C31×#2264 | 2 |
| C2×C31×SD64 | 2 |
| C31×#2222 | 2 |
| C31×#1419 | 2 |
| C31×#1417 | 2 |
| C31×#1401 | 2 |
| #13671 | 31 |