Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1000 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1000 conjugacy classes of subgroups — too many to draw. Only its 224 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 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C31×#120 | C2 | semidirect |
| 2. C31×#394 | C2 | semidirect |
| 3. C31×#390 | C2 | semidirect |
| 4. C25×C31 | C22 | semidirect |
| 8. C2×C4⋊C4×C31 | C22 | semidirect |
| 9. C2×C22⋊C4×C31 | C22 | semidirect |
| 10. C2×C22⋊C4×C31 | C22 | semidirect |
| 11. C2×C42×C31 | C22 | semidirect |
| 12. C31×#95 | C22 | semidirect |
| 21. C2×D4×C31 | D4 | semidirect |
| 44. #2679 | C31 | direct (N × H) |
| 56. C2×#120 | C2×C31 | semidirect |
| 57. #394 | C2×C31 | semidirect |
| 58. #390 | C2×C31 | semidirect |
| 63. C25 | C22×C31 | semidirect |
| 67. C2×C4⋊C4 | C22×C31 | semidirect |
| 68. C2×C22⋊C4 | C22×C31 | semidirect |
| 69. C2×C22⋊C4 | C22×C31 | semidirect |
| 70. C2×C42 | C22×C31 | semidirect |
| 71. #95 | C22×C31 | semidirect |
| 72. C31 | #2679 | direct (N × H) |
| 81. C2×D4 | D4×C31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C31×#120 | 2 |
| C31×#394 | 2 |
| C31×#390 | 2 |
| #2679 | 31 |