Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
216 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #1181 |
| commutator, hypocenter | C29 | C2×C4×C16 |
| Frattini | C8 | C22×#1181 |
| Fitting | C2×C16×C29 | C4 |
| socle | C22×C29 | C4×C8 |
| prime radical | C22×D29 | C2×C8 |
| cosocle | C8×D29 | C23 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C2×C16 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C16×#1181 | C2 | direct (N × H) |
| 8. C2×#90770 | C4 | semidirect |
| 11. D29⋊C16 | C4 | semidirect |
| 13. C2×C16×C29 | C4 | semidirect |
| 14. C2×#90768 | C4 | semidirect |
| 15. C16×D29 | C4 | semidirect |
| 30. #90770 | C2×C4 | semidirect |
| 31. C16×C29 | C2×C4 | semidirect |
| 32. #90768 | C2×C4 | semidirect |
| 34. C2×#1181 | C16 | direct (N × H) |
| 52. #1181 | C2×C16 | direct (N × H) |
| 61. C2×C29 | C4×C16 | semidirect |
| 63. D29 | C4×C16 | semidirect |
| 74. C2×C16 | #1181 | direct (N × H) |
| 77. C29 | C2×C4×C16 | semidirect |
| 93. C16 | C2×#1181 | direct (N × H) |
| 119. C2 | C16×#1181 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D29⋊C16 | 2 |
| C2×C8×#1181 | 2 |
| C16×#1181 | 2 |
| C2×C16×D29 | 2 |
| C2×C4×C16 | 29 |