Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
196 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×#1181 |
| commutator, socle | C2×C29 | C2×C4×C8 |
| Fitting | C29×M32 | C4 |
| prime radical | C22×D29 | C2×C8 |
| cosocle | C8×D29 | C23 |
| hypercenter | M32 | #1181 |
| hypocenter | C29 | C4×M32 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C8 ◁ M32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14272050 | C2 | semidirect |
| 4. C16×#1181 | C2 | semidirect |
| 9. #11745214 | C4 | semidirect |
| 14. #11745206 | C4 | semidirect |
| 16. C29×M32 | C4 | semidirect |
| 17. #11745160 | C4 | semidirect |
| 18. #11745146 | C4 | semidirect |
| 35. #90770 | C2×C4 | semidirect |
| 36. C16×C29 | C2×C4 | semidirect |
| 37. #90768 | C2×C4 | semidirect |
| 60. #1181 | M32 | direct (N × H) |
| 81. M32 | #1181 | direct (N × H) |
| 88. C29 | C4×M32 | semidirect |
| 106. C16 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D29⋊M32 | 2 |
| C2×C8×#1181 | 2 |
| #14272050 | 2 |
| C16×#1181 | 2 |
| M32×D29 | 2 |
| C4×M32 | 29 |