Finite Group DatabasebetaFinite Group DatabasebetaOrder 38634.
16 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×C47×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | D6439 | — | 3 | 1 | no | maximal, Hall |
| 3 | C47×C137 | D3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 4 | D411 | — | 47 | 1 | no | maximal, Hall |
| 5 | C3×C137 | D47 | 1 | 1 | yes | characteristic, complemented, Hall |
| 6 | D141 | — | 137 | 1 | no | maximal, Hall |
| 7 | D137 | — | 141 | 1 | no | Hall |
| 8 | C3×C47 | D137 | 1 | 1 | yes | characteristic, complemented, Hall |
| 9 | C137 | D141 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 10 | D47 | — | 411 | 1 | no | Hall |
| 11 | C47 | D411 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 12 | D3 | — | 6439 | 1 | no | Hall |
| 13 | C3 | D6439 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 14 | C2 | — | 19317 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C47×C137 | C2 |
| LCS | G ▷ C3×C47×C137 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C47×C137 | C2 | semidirect |
| 3. C47×C137 | D3 | semidirect |
| 5. C3×C137 | D47 | semidirect |
| 8. C3×C47 | D137 | semidirect |
| 9. C137 | D141 | semidirect |
| 11. C47 | D411 | semidirect |
| 13. C3 | D6439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C47×C137 | 2 |
| D6439 | 3 |
| D411 | 47 |
| D141 | 137 |