Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
314 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 314 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, socle | C22×C31 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C31 |
| prime radical | C31×#1667 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C42×C31 ◁ C8×D4×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C31×#3338 | C2 | semidirect |
| 2. C31×#2240 | C2 | semidirect |
| 3. C31×#2207 | C2 | semidirect |
| 5. C31×#1365 | C2 | semidirect |
| 6. C31×#1332 | C2 | semidirect |
| 7. C31×D4⋊C16 | C2 | semidirect |
| 86. #12342 | C31 | direct (N × H) |
| 98. D4×C31 | SD32 | semidirect |
| 114. #3338 | C2×C31 | semidirect |
| 115. #2240 | C2×C31 | semidirect |
| 116. #2207 | C2×C31 | semidirect |
| 118. #1365 | C2×C31 | semidirect |
| 119. #1332 | C2×C31 | semidirect |
| 120. D4⋊C16 | C2×C31 | semidirect |
| 187. C31 | #12342 | direct (N × H) |
| 232. D4 | C31×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#3338 | 2 |
| C31×#2240 | 2 |
| C31×#2207 | 2 |
| C31×#1667 | 2 |
| C31×#1365 | 2 |
| C31×#1332 | 2 |
| C31×D4⋊C16 | 2 |
| #12342 | 31 |