Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
684 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C31 |
| prime radical | C31×#2657 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C31×#3215 | C2 | semidirect |
| 2. C31×#3138 | C2 | semidirect |
| 4. C31×#1555 | C2 | semidirect |
| 5. C31×#1527 | C2 | semidirect |
| 6. C31×#1506 | C2 | semidirect |
| 7. C31×#1300 | C2 | semidirect |
| 40. C31×C4⋊Q8 | D4 | semidirect |
| 41. C31×C4⋊Q8 | D4 | semidirect |
| 64. C31×C4⋊C8 | D4 | semidirect |
| 73. C31×#97 | D4 | semidirect |
| 129. #10096 | C31 | direct (N × H) |
| 172. #3215 | C2×C31 | semidirect |
| 173. #3138 | C2×C31 | semidirect |
| 175. #1555 | C2×C31 | semidirect |
| 176. #1527 | C2×C31 | semidirect |
| 177. #1506 | C2×C31 | semidirect |
| 178. #1300 | C2×C31 | semidirect |
| 240. C4⋊Q8 | D4×C31 | semidirect |
| 241. C4⋊Q8 | D4×C31 | semidirect |
| 264. C4⋊C8 | D4×C31 | semidirect |
| 273. #97 | D4×C31 | semidirect |
| 277. C31 | #10096 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#3215 | 2 |
| C31×#3138 | 2 |
| C31×#2657 | 2 |
| C31×#1555 | 2 |
| C31×#1527 | 2 |
| C31×#1506 | 2 |
| C31×#1300 | 2 |
| #10096 | 31 |