Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
500 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 229 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D37 |
| commutator, socle | C22×C37 | C23×C4 |
| Fitting, prime radical | C37×#532 | C2 |
| cosocle | C2×C4×C37 | C24 |
| hypercenter | #532 | D37 |
| hypocenter | C37 | #2931 |
| LCS | G ▷ C22×C37 ▷ C37 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11924543 | C2 | semidirect |
| 2. #14557611 | C2 | semidirect |
| 3. D4×#64436 | C2 | semidirect |
| 4. #14557557 | C2 | semidirect |
| 5. #14557500 | C2 | semidirect |
| 6. C2×C4×#64436 | C2 | semidirect |
| 43. C2×#64436 | D4 | semidirect |
| 76. C4×C37 | #131 | semidirect |
| 91. C37 | #2931 | semidirect |
| 160. C4 | #11924543 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924543 | 2 |
| #14557611 | 2 |
| D4×#64436 | 2 |
| #14557557 | 2 |
| #14557500 | 2 |
| C2×C4×#64436 | 2 |
| C37×#532 | 2 |
| #2931 | 37 |