Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
368 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C31 | #102 |
| commutator | C2×C8 | C22×C4×C31 |
| Frattini, cosocle | C22×C8 | C23×C31 |
| socle | C22×C31 | C2×#102 |
| prime radical | C31×#3169 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C31 ◁ C2×C42×C31 ◁ C2×C4×C8×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C31×#2162 | C2 | semidirect |
| 3. C4×C31×#108 | C2 | semidirect |
| 4. C31×#1349 | C2 | semidirect |
| 76. #11747 | C31 | direct (N × H) |
| 103. #2162 | C2×C31 | semidirect |
| 104. C4×#108 | C2×C31 | semidirect |
| 105. #1349 | C2×C31 | semidirect |
| 167. C31 | #11747 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#3169 | 2 |
| C31×#2162 | 2 |
| C4×C31×#108 | 2 |
| C31×#1349 | 2 |
| #11747 | 31 |