Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
262 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C37 | C2×#99 |
| commutator | C2×C4 | C22×C4×C37 |
| Frattini, cosocle | C2×Q8 | C23×C37 |
| prime radical | C37×#535 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C37 ◁ C2×C4×C37 ◁ C2×#41×C37 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C37×#413 | C2 | semidirect |
| 3. C37×#355 | C2 | semidirect |
| 12. #101×C37 | C22 | semidirect |
| 63. #2134 | C37 | direct (N × H) |
| 70. #413 | C2×C37 | semidirect |
| 71. #355 | C2×C37 | semidirect |
| 72. C37 | #2134 | direct (N × H) |
| 81. #101 | C22×C37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C37×#535 | 2 |
| C37×#413 | 2 |
| C37×#355 | 2 |
| #2134 | 37 |