Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
346 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#3866 |
| commutator, socle | C22×C37 | C23×C4 |
| Fitting, prime radical | #121×C37 | C4 |
| cosocle | C2×Dic37 | C24 |
| hypercenter | #121 | #3866 |
| hypocenter | C37 | #2995 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14558585 | C2 | semidirect |
| 2. #14558568 | C2 | semidirect |
| 3. #14558564 | C2 | semidirect |
| 4. #14558564 | C2 | semidirect |
| 5. #14558557 | C2 | semidirect |
| 6. #14558553 | C2 | semidirect |
| 7. #14558539 | C2 | semidirect |
| 8. #14558536 | C2 | semidirect |
| 124. C37 | #2995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558585 | 2 |
| #14558568 | 2 |
| #14558564 | 2 |
| #14558557 | 2 |
| #14558553 | 2 |
| #14558539 | 2 |
| #14558536 | 2 |
| #14558064 | 2 |
| #2995 | 37 |