Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
228 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#3866 |
| commutator, socle, prime radical | C23×C37 | C22×C4 |
| Fitting | #95×C37 | C4 |
| cosocle | C22×Dic37 | C23 |
| hypercenter | #95 | #3866 |
| hypocenter | C37 | #1917 |
| LCS | G ▷ C23×C37 ▷ C37 | |
| UCS | C1 ◁ C23 ◁ #95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 109. C37 | #1917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#64438 | 2 |
| C2×#11924591 | 2 |
| #14558399 | 2 |
| #14557384 | 2 |
| #1917 | 37 |