Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
5134 conjugacy classes of subgroups; only the 494 normal subgroups are shown.
This group has 5134 conjugacy classes of subgroups — too many to draw. Only its 494 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C31 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C31 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C31×#127 | C2 | semidirect |
| 2. C22×C31×#120 | C2 | semidirect |
| 3. C2×C31×#392 | C2 | semidirect |
| 4. C31×#1438 | C2 | semidirect |
| 5. C31×#1437 | C2 | semidirect |
| 9. C23×D4×C31 | C22 | semidirect |
| 15. C22×C22⋊C4×C31 | C22 | semidirect |
| 16. C22×C42×C31 | C22 | semidirect |
| 18. C2×C31×#95 | C22 | semidirect |
| 37. C22×D4×C31 | D4 | semidirect |
| 48. C2×C22⋊C4×C31 | D4 | semidirect |
| 99. #15258 | C31 | direct (N × H) |
| 135. C23×C31 | #127 | semidirect |
| 150. C2×C4×C31 | #120 | semidirect |
| 151. C22×#127 | C2×C31 | semidirect |
| 152. C22×#120 | C2×C31 | semidirect |
| 153. C2×#392 | C2×C31 | semidirect |
| 154. #1438 | C2×C31 | semidirect |
| 155. #1437 | C2×C31 | semidirect |
| 183. C23×D4 | C22×C31 | semidirect |
| 189. C22×C22⋊C4 | C22×C31 | semidirect |
| 190. C22×C42 | C22×C31 | semidirect |
| 192. C2×#95 | C22×C31 | semidirect |
| 217. C22×D4 | D4×C31 | semidirect |
| 228. C2×C22⋊C4 | D4×C31 | semidirect |
| 231. C31 | #15258 | direct (N × H) |
| 315. C23 | C31×#127 | semidirect |
| 330. C2×C4 | C31×#120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C31×#127 | 2 |
| C22×C31×#120 | 2 |
| C2×C31×#392 | 2 |
| C31×#1438 | 2 |
| C31×#1437 | 2 |
| #15258 | 31 |