Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
760 conjugacy classes of subgroups; only the 418 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 418 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | #1181 |
| commutator, hypocenter | C29 | C22×C4×C8 |
| Frattini | C4 | C23×#1181 |
| Fitting | C22×C8×C29 | C4 |
| socle | C23×C29 | C42 |
| prime radical | C23×D29 | C2×C4 |
| cosocle | C4×D29 | C24 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C22×C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C8×#1181 | C2 | direct (N × H) |
| 7. C22×#6599 | C4 | semidirect |
| 10. C2×D29⋊C8 | C4 | semidirect |
| 12. C22×C8×C29 | C4 | semidirect |
| 13. C22×#6597 | C4 | semidirect |
| 14. C2×C8×D29 | C4 | semidirect |
| 16. C8×#1181 | C22 | direct (N × H) |
| 18. C22×#1181 | C8 | direct (N × H) |
| 26. C2×#6599 | C2×C4 | semidirect |
| 29. D29⋊C8 | C2×C4 | semidirect |
| 31. C2×C8×C29 | C2×C4 | semidirect |
| 32. C2×#6597 | C2×C4 | semidirect |
| 33. C8×D29 | C2×C4 | semidirect |
| 39. C2×#1181 | C2×C8 | direct (N × H) |
| 50. #6599 | C22×C4 | semidirect |
| 51. C8×C29 | C22×C4 | semidirect |
| 52. #6597 | C22×C4 | semidirect |
| 54. C22×C29 | C4×C8 | semidirect |
| 56. C2×D29 | C4×C8 | semidirect |
| 60. #1181 | C22×C8 | direct (N × H) |
| 69. C2×C29 | C2×C4×C8 | semidirect |
| 71. D29 | C2×C4×C8 | semidirect |
| 81. C22×C8 | #1181 | direct (N × H) |
| 85. C29 | C22×C4×C8 | semidirect |
| 101. C2×C8 | C2×#1181 | direct (N × H) |
| 121. C8 | C22×#1181 | direct (N × H) |
| 126. C22 | C8×#1181 | direct (N × H) |
| 135. C2 | C2×C8×#1181 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D29⋊C8 | 2 |
| C22×C4×#1181 | 2 |
| C2×C8×#1181 | 2 |
| C22×C8×D29 | 2 |
| C22×C4×C8 | 29 |