Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
178 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C22×D37 |
| commutator, socle | C22×C37 | C2×C42 |
| Fitting | C37×#431 | C2 |
| prime radical | C23×C37 | C42 |
| cosocle | C42×C37 | C23 |
| hypercenter | #431 | D37 |
| hypocenter | C37 | #1454 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C42 ◁ #431 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14557255 | C2 | semidirect |
| 4. #14557255 | C2 | semidirect |
| 5. #14557254 | C2 | semidirect |
| 6. C8×#64436 | C2 | semidirect |
| 72. C37 | #1454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14557586 | 2 |
| #14557255 | 2 |
| #14557254 | 2 |
| C8×#64436 | 2 |
| C37×#431 | 2 |
| #1454 | 37 |