Finite Group DatabasebetaFinite Group DatabasebetaOrder 7936.
2080 conjugacy classes of subgroups; only the 302 normal subgroups are shown.
This group has 2080 conjugacy classes of subgroups — too many to draw. Only its 302 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C31 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ C22×#41×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C31×#535 | C2 | semidirect |
| 2. C2×C31×#447 | C2 | semidirect |
| 3. C31×#1999 | C2 | semidirect |
| 4. C31×#1875 | C2 | semidirect |
| 5. C31×#1780 | C2 | semidirect |
| 7. C23×D4×C31 | C22 | semidirect |
| 13. C2×C31×#121 | C22 | semidirect |
| 16. C2×C31×#117 | C22 | semidirect |
| 18. C2×C31×#102 | C22 | semidirect |
| 19. C2×C31×C22⋊C8 | C22 | semidirect |
| 20. C2×C31×C22⋊C8 | C22 | semidirect |
| 21. C31×#340 | C22 | semidirect |
| 45. C31×#121 | D4 | semidirect |
| 102. #23925 | C31 | direct (N × H) |
| 140. C2×#535 | C2×C31 | semidirect |
| 141. C2×#447 | C2×C31 | semidirect |
| 142. #1999 | C2×C31 | semidirect |
| 143. #1875 | C2×C31 | semidirect |
| 144. #1780 | C2×C31 | semidirect |
| 166. C23×D4 | C22×C31 | semidirect |
| 172. C2×#121 | C22×C31 | semidirect |
| 175. C2×#117 | C22×C31 | semidirect |
| 177. C2×#102 | C22×C31 | semidirect |
| 178. C2×C22⋊C8 | C22×C31 | semidirect |
| 179. C2×C22⋊C8 | C22×C31 | semidirect |
| 180. #340 | C22×C31 | semidirect |
| 210. #121 | D4×C31 | semidirect |
| 222. C31 | #23925 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C31×#535 | 2 |
| C2×C31×#447 | 2 |
| C31×#1999 | 2 |
| C31×#1875 | 2 |
| C31×#1780 | 2 |
| #23925 | 31 |